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<image>What is the measure of angle BOE in circle O, if BC is the diameter, AB intersects the circle at point E, AC intersects the circle at point D, AD equals CD, and angle A measures 70 degrees? | 100° | |
<image>Given that BD is the diameter of circle O and point A and C lie on the circle with CD equal to OB, what is the measure of angle BAC? | 60° | |
<image>In the given diagram, quadrilateral ABCD is inscribed in circle O, and angle A measures 100 degrees. What is the measure of angle BOD? | 160° | |
<image>If triangle OAD is congruent to triangle OBC and angle O measures 65.0 degrees while angle C measures 20.0 degrees, what is the degree measure of angle OAD? | 95° | |
<image>If point A, B, and C lie on circle O and angle B measures 32 degrees, what is the measure of angle AOC? | 64° | |
<image>In the given illustration, circle O has diameter AB, with points C and D situated on the circle. If angle BDC measures 36 degrees, what is the degree measurement of angle ABC? | 54° | |
<image>In the given illustration, if BD serves as the diameter of circle O and is perpendicular to AC at point E, and angle AOC is 100 degrees, what is the measure of angle BDC? | 25° | |
<image>In the given illustration, if points A, B, and C lie on circle O and the measure of angle AOB is 82 degrees, what is the degree measure of angle C? | 41° | |
<image>What is the measure of angle D if AB is the diameter of circle O, and points C and D lie on circle O, with angle CAB equal to 20 degrees? | 110° | |
<image>On circle O, points A, B, C, and D are positioned such that OA is perpendicular to BC at point E. If angle ADC measures 35°, what is the degree measure of angle OBC? | 20° | |
<image>In the given diagram, it is depicted that AB serves as the diameter of circle O, and CD acts as a chord of circle O. If angle BAD measures 56°, what is the measurement of angle ACD? | 34° | |
<image>In the given diagram, circle O shows radius OC being perpendicular to AB at point H. If angle OAB is 40 degrees, what is the measure of angle ABC? | 25° | |
<image>As shown in the figure, AB is the diameter of circle O. C and D are two points on circle O, and point C is the midpoint of the arc BAD. Connect CD, CB, OD, and CD intersects AB at point F. If angle ABC=20°, then the degree of angle AOD is (). | 100° | |
<image>In the given diagram, triangle ABC is inscribed in circle O with angle A measuring 50°. The midpoint of side BC is denoted by E. What is the measure of angle D formed when extending OE to intersect circle O at point D and connecting BD? | 65° | |
<image>Given an isosceles triangle ABC with a vertex angle BAC measuring 50°, a semicircle with AB as the diameter intersects BC and AC at points D and E, what is the measure of angle DE? | 50° | |
<image>In the given diagram, the line segment AB serves as the diameter of circle O. Chord CD is perpendicular to AB at point E. If AC, OC, and OD are connected, and angle COD measures 80 degrees, what is the measure of angle A? | 20° | |
<image>As shown in the picture, in circle O, AB is a diameter, and C and D are two points on circle O. OC is parallel to AD. If angle DAC = 25°, then the degree of angle BOC is () | 50° | |
<image>What is the measure of angle ADC if AB is the diameter of a semicircle and C, D are two points on the semicircle such that angle CAB measures 24 degrees? | 114° | |
<image>As shown in the figure, in circle O, AB is the diameter, angle A = 50°, point D is the midpoint of chord AC, and point E is any point on BC. The possible size of angle CED is (). | 40° | |
<image>In the given diagram, the line AB is a tangent to circle O at point A, while OB intersects circle O at point C, and point D lies on the major arc AC. If angle B measures 30 degrees, what is the degree measure of angle ADC? | 30° | |
<image>In the given diagram, quadrilateral ABCD is inscribed in circle O. If the measure of angle DCE is 65 degrees, what is the degree measure of angle A? | 65° | |
<image>In the given diagram, the chords AB and CD intersect at point E, and the measure of arc AD is equal to the measure of arc CB. If angle C measures 50 degrees, what is the degree measure of angle CEB? | 100° | |
<image>In the figure, triangle ABC is circumscribed about circle O, AB=AC, BO is connected and extended to intersect AC at point D. If angle A=50°, then the measure of angle BDC is (). | 75° | |
<image>If points A, B, C, and D lie on circle O, with AB equal to AC and BD being a diameter of circle O, and CD being connected, what is the measure of angle ACD if angle A measures 36°? | 18° | |
<image>Given the diagram with circle O, if angle BOD measures 80 degrees, what is the measure of angle BCD? | 140° | |
<image>In the given diagram, if AB is a chord of circle O and OC is perpendicular to AB, intersecting circle O at point C, and angle AOB measures 80 degrees, what is the degree measure of angle ABC? | 20° | |
<image>In the given diagram, the line AB is tangent to circle O at point A, and the line OB intersects circle O at point C. Additionally, point D lies on circle O. If angle ABO is measured at 20 degrees, what is the degree measure of angle ADC? | 35° | |
<image>What is the measure of angle APC if point P lies on line segment ED, and circle O is the circumcircle of the regular pentagon ABCDE? | 72° | |
<image>In the provided diagram, circle O has diameter AB and point C lies on the circle. If angle OCA measures 25.0 degrees, what is the measure of angle BOC? | 50° | |
<image>If AB is the diameter of circle O and points C and D lie on circle O, with OD being perpendicular to AC, and angle COB measures 20°, what is the degree measure of angle ACD? | 40° | |
<image>If PA and PB are tangents to circle O at points A and B, and C is a moving point on arc AB, what is the measure of angle ACB if angle P measures 40 degrees? | 70° | |
<image>Points A, B, C, and D lie on circle O, with O as the center. The quadrilateral OABC is formed by connecting AD, BD, and consecutively connecting O, A, B, C. Given that OA is equal to BC, and OC is equal to AB, what is the measure of angle D? | 30° | |
<image>In the given diagram, the line segment AB represents the diameter of circle O. A tangent, DA, is drawn from point D to circle O at point A, and the line DO intersects circle O at point C. When angle D measures 40 degrees, what is the measurement of angle B? | 25° | |
<image>In the given illustration, circle O has diameter AB. Points C and D are situated on circle O, on opposite sides of AB. Segments OC, CD, and DA are connected. If angle BOC measures 130 degrees, what is the measure of angle D? | 25° | |
<image>If quadrilateral ADCB is inscribed in circle O and angle AOB measures 122 degrees, what is the measure of angle ACB? | 119° | |
<image>As shown in the diagram, AB is the diameter of circle O. CB is tangent to circle O at point B. AC intersects circle O at point D. OD is connected. If angle C = 58°, then the degree of angle BOD is () | 64° | |
<image>If PA is a tangent to circle O at point A and the extension of PO intersects circle O at point C, and if angle P measures 40 degrees, what is the measure of angle CQA when point Q is a moving point on line AC? | 115° | |
<image>Triangle ABC is inscribed in circle O, where the bisector of the external angle BAE intersects circle O at point D, and A is the midpoint of arc CD. If angle ABC measures 28°, what is the measure of angle ACB? | 84° | |
<image>As shown in the diagram, in circle O, Q is an external point of circle O. QA and QB are tangent to circle O at points A and B, respectively. C and D are two points on circle O. If angle Q is 110°, then angle B plus angle D equals () | 215° | |
<image>As shown in the diagram, PA and PB are tangent to circle O at points A and B respectively. Angle P is 72 degrees. Then the degree of angle C is (). | 54° | |
<image>In the given illustration of circle O, where AB, BC, and CD are all equal, and angle AOB measures 40 degrees, what is the degree measure of angle CAD? | 20° | |
<image>If AB is the diameter of circle O and points C and D lie on the circle, with angle BAC measuring 35 degrees, what is the measure of angle ADC? | 55° | |
<image>In the given diagram, the line AB is tangent to circle O at point A. Line OB intersects circle O at point C, and point D lies on circle O. When connecting points AD, CD, and OA, if angle ADC measures 30 degrees, what is the measure of angle ABO? | 30° | |
<image>In the given illustration, in circle O, the radius AO is perpendicular to OB. Point P lies on the major arc APB, and the midpoint of AB is denoted as C. If we connect AP and CP, what is the measure of angle APC? | 22.5° | |
<image>In the given diagram, four points A, B, C, and D lie on circle O. The measure of angle AOC is 140 degrees and point B is the midpoint of AC. What is the degree measure of angle D? | 35° | |
<image>What is the measure of angle BAD if AB is the diameter of circle O, point C lies on circle O with CO perpendicular to AB at point O, and chord CD intersects AB at point E with angle AEC measuring 64°? | 19° | |
<image>What is the measure of angle D if triangle ABC is inscribed in circle O, angle BAC measures 50 degrees, and AD is drawn parallel to BC passing through point A, intersecting the extension of CO at point D? | 40° | |
<image>What is the measure of angle ADC if points A, B, C, and D are all on circle O, and AB and CD intersect at an external point E of circle O, with angle BCD measuring 25° and angle E measuring 39°? | 64° | |
<image>What is the degree measure of angle DCB if triangle CAB undergoes a clockwise rotation around point C by 34.0 degrees to form triangle CDE, and angle ACE is measured at 88.0 degrees? | 20° | |
<image>In the given illustration, within circle O, point D serves as the midpoint of line segment AB, where CD represents the diameter of circle O. Additionally, line segment AE is parallel to BC and intersects circle O at point E. By extending CE, what is the measure of angle DCB if angle ECD is 50 degrees? | 20° | |
<image>As shown in the diagram, BD is the diameter of circle O. Points A and C are on circle O, with AB=AD. AC intersects BD at point G. If angle COD=120°, then the degree measure of angle AGB is (). | 105° | |
<image>In the given diagram, the tangent PA touches circle O at point A. If the line PO intersects circle O at point B, and point C lies on circle O, and angle P measures 45 degrees, what is the degree measure of angle ACB? | 22.5° | |
<image>Given the diagram depicting triangle ABC inscribed in circle O, where angle ABC measures 60 degrees, what is the measure of angle AOC? | 120° | |
<image>What is the measure of angle ACB if angle ABO measures 25 degrees and O is the circumcircle of triangle ABC? | 65° | |
<image>What is the measure of angle AFD if angle BAC is 36 degrees, point O lies on side AB, and circle O is tangent to side AC at point D and intersects side AB at points E and F? | 27° | |
<image>In the given diagram, triangle ABC has its circumcircle denoted as circle O, with AD serving as the diameter. If the measure of angle BCA is 50°, what is the measure of angle BAD? | 40° | |
<image>In the given diagram, triangle ABC is inscribed in circle O, and AD is the diameter of the circle. If angle CAD measures 50 degrees, what is the degree measure of angle ABC? | 40° | |
<image>In the given figure, triangle BCD is inscribed in circle O, and angle D measures 70 degrees. Line OA is perpendicular to BC and intersects circle O at point A. What is the measure of angle OAC when AC is connected? | 55° | |
<image>In the given illustration, circle O has diameter AB, and points C and D lie on the circle. If angle ABD measures 54°, what is the degree measure of angle C? | 36° | |
<image>What is the angle measure of BOA' after rotating the line segment OA counterclockwise around point O by 120 degrees, if angle B measures 40 degrees and BA is tangent to circle O at point A? | 70° | |
<image>In the given diagram, triangle ABC is inscribed in circle O. If the measure of angle OBC is 35°, what is the measure of angle BAC? | 55° | |
<image>In the given diagram, circle O is the circumcircle of triangle ABC. If angle OAB measures 25°, what is the measure of angle ACB? | 65° | |
<image>As shown in the figure, triangle ABC is circumscribed by circle O, and the radius of circle O is 2. If angle ACB = 45°, then AB is () | 2√{2} | |
<image>In the provided diagram, triangle ABC is inscribed in circle O, with the measure of angle A being 74 degrees. What is the measure of angle OBC? | 16° | |
<image>What is the measure of angle COB in circle O if chord CD intersects diameter AB at point E, and angle ABD is 20 degrees while angle AED is 80 degrees? | 120° | |
<image>If points A, B, and C are all located on circle O and the measure of angle O is 70 degrees, what is the measurement of angle C? | 35° | |
<image>What is the measure of angle C if AB is the diameter of circle O and point C lies on circle O? | 90° | |
<image>In the given figure, circle O is intersected by OB at point C, with AB being a tangent to the circle at point A. Additionally, point D lies on circle O and lines AD, CD, and OA are connected. If angle ADC measures 25°, what is the degree measure of angle ABO? | 40° | |
<image>In the given diagram, quadrilateral ABCD is inscribed in circle O, and one of its exterior angles, angle CBE, measures 56°. What is the measure of angle AOC? | 112° | |
<image>In the given diagram, circle O has diameter AB, and points C and D lie on the circle. If angle ABD measures 63° and angle DCO measures 24°, what is the degree measure of angle BDC? | 39° | |
<image>What is the measure of angle ADB if point C is the midpoint of chord AB in circle O, and angle COB measures 56 degrees with point D being an arbitrary point on AB? | 124° | |
<image>If points C and D are located on a semicircle with AB as the diameter and angle ADC measures 120 degrees, and point E is an arbitrary point on AD, what is the measure of angle BEC when BE and CE are connected? | 30° | |
<image>If angle ABC is 25 degrees and points A, B, and C are all located on circle O, what is the measure of angle AOC? | 50° | |
<image>If points A, B, and C lie on circle O, and angle ACB measures 43 degrees, what is the measure of angle AOB? | 86° | |
<image>What is the degree measure of angle OAB if BC is the diameter of circle O and AB is a chord of circle O when angle AOC measures 60 degrees? | 30° | |
<image>Given that AB is the diameter of circle O, with D as the midpoint of the semicircle and point C located on the other half of the circle, and connecting OD, CD, and BC, what can be concluded from the diagram? | ||
<image>In the given figure, a tangent line AB touches circle O at point A, and line BO intersects circle O at point C. Additionally, point D is on circle O. If the measure of angle ADC is 27°, what is the measure of angle B? | 36° | |
<image>What is the measure of angle CBD if triangle ABC is circumscribed about circle O, angle A measures 50 degrees, and OD is perpendicular to BC with the foot at E? | 25° | |
<image>In the given diagram, all points A, B, and C lie on circle O. If the measure of angle ACB is 70 degrees, what is the measure of angle OAB? | 20° | |
<image>What is the degree measure of angle BDE if AB is the diameter of circle O and points C, D, and E lie on circle O, with angle ACE measuring 20°? | 110° | |
<image>In the figure, if the circle O is tangent to the two sides AE and CD of the regular pentagon ABCDE at points A and C, then the degree of angle AOC is (). | 144° | |
<image>In the given illustration, the quadrilateral ABCD is circumscribed in the circle O. A point P, which is not coincident with points A and D, is arbitrarily chosen on side AD. What could be the measure of angle APC if angle B is 120 degrees? | 60° | |
<image>In the provided figure, circle O has diameter AB and tangent BC. If angle BAC measures 35°, what is the measure of angle ACB? | 55° | |
<image>In the given diagram, quadrilateral ABCD is inscribed in circle O. The diameter BE is part of circle O and AE is connected to it. If the measure of angle BCD is twice the measure of angle BAD, then what is the degree measure of angle DAE? | 30° | |
<image>In the given diagram, line AB is tangent to circle O at point C, and line AO meets circle O at point D. If angle AOC measures 50°, what is the degree measurement of angle ACD? | 25° | |
<image>In the given illustration, lines PA and PB are tangents to circle O at points A and B. If angle P measures 70°, what is the measure of angle ABO? | 35° | |
<image>What is the measure of angle OCD in circle O, where AB is the tangent at point A, OB intersects circle O at point C, and a line parallel to OB passing through point A intersects circle O at point D, if angle B measures 50 degrees? | 20° | |
<image>In the given figure, if AB is parallel to CD and AD bisects angle BAE, with angle D measuring 38.0 degrees, what is the degree measure of angle AEC? | 76° | |
<image>What is the measure of angle BDC if points C and D are on diameters AB of circle O and angle ABC is 25 degrees? | 65° | |
<image>In the given diagram, points A, B, and C lie on the circumference of circle O with a radius of 1. If the length of AB is √2 and the measure of angle CAB is 30 degrees, what is the degree measure of angle ABC? | 105° | |
<image>What is the measure of angle BED if AB and CD are perpendicular chords of circle O, intersecting at point P, and angle ABC measures 70 degrees, with point E lying on the circle? | 20° | |
<image>In the given diagram, circle O has diameter AB and point C lies on the circle. If angle OCA measures 26 degrees, what is the measure of angle BOC? | 52° | |
<image>What is the measure of angle C if AB is the diameter of circle O, point C lies on circle O, and angle BOC measures 60 degrees? | 30° | |
<image>In the provided diagram, if points A, B, and C all lie on the circle O and angle BAC measures 54°, what is the measure of angle BOC? | 108° | |
<image>In the given diagram, quadrilateral ABCD is inscribed in circle O. If the exterior angle DCE measures 64°, what is the degree measurement of angle BOD? | 128° | |
<image>As shown in the figure, points A, B, and C are three points on circle O. If angle AOC = 90° and angle BAC = 30°, the size of angle AOB is (). | 30° | |
<image>If line segment AB serves as the diameter of circle O, and chord CD is perpendicular to AB at point E, such that the length of CD is twice the length of OE, what is the measure of angle BCD? | 22.5° | |
<image>What is the measure of angle ACB if the lines PA and PB touch circle O at points A and B, respectively, and angle P measures 70 degrees? | 125° | |
<image>Given points A, B, C, D, and E on circle O, where AB is equal to CD and angle AOB measures 42 degrees, what is the measure of angle CED? | 21° | |
<image>As shown in the diagram, the three vertices of equilateral triangle ABC are all on circle O, and AD is the diameter of circle O. If OA = 3, then the length of minor arc BD is (). | π |
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