images
images listlengths 1
1
| problem
stringlengths 27
925
| answer
stringlengths 1
104
|
|---|---|---|
<image>In the figure, O is the intersection point of the diagonals of rectangle ABCD, DE bisects ∠ADC and intersects BC at point E. If ∠BDE = 15°, then ∠COE = ___ degrees
| 75 |
|
<image>As shown in the figure, $AB\text{//}EF\text{//}DC$, $AD\text{//}BC$, and $EF$ intersects $AC$ at point $G$. How many pairs of similar triangles are there?
| 6 |
|
<image>As shown in the figure, given $$AB=CD=AE=BC+DE=2$$, $$∠ABC=∠AED=90^{\circ}$$, then the area of pentagon $$ABCDE$$ is ___.
| $$4$$ |
|
<image>Given squares $$ABCD$$, $$CEFG$$, and $$PQFH$$ are placed as shown in the figure, and the side length of square $$CEFG$$ is $$4$$. Points $$A$$, $$G$$, and $$P$$ are collinear. Connecting $$AE$$ and $$EP$$, the area of $$\triangle AEP$$ is ___.
| $$16$$ |
|
<image>As shown in the figure, $$B$$ and $$C$$ are the trisection points of line segment $$AD$$. The maximum number of distinct non-zero vectors that can be determined by using the points in the figure as starting and ending points is ___.
| $$6$$ |
|
<image>As shown in the figure, in a $$5\times 4$$ grid paper, each small square has a side length of $$1$$. Points $$O$$, $$A$$, and $$B$$ are located at the intersections (lattice points) of the grid lines. Find a point $$C$$ in the fourth quadrant on a lattice point such that the area of $$\triangle ABC$$ is $$3$$. How many such points $$C$$ are there?
| $$3$$ |
|
<image>As shown in the figure, in $$\triangle ABC$$, $$\angle C = 25^{\circ}$$, $$\angle B = 85^{\circ}$$, a circle passing through points $$A$$ and $$B$$ intersects sides $$AC$$ and $$BC$$ at points $$E$$ and $$D$$, respectively. Then $$\angle EDC = $$___.
| $$70^{\circ}$$ |
|
<image>As shown in the figure, DE∥BC, DE:BC = 3:4, then AE:CE =.
| 3 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.