Triangles
In triangle ABC, ∠A=30 ∠B=50. Point D lies on AC such that ∠ABD=20. Find ∠BDC.
40
A chord of a circle subtends a 40 degree angle at the center. What is the measure of the angle subtended by the same chord at a point on the circle?
20 degrees
Two similar triangles have side lengths in the ratio 2:5. If the smaller triangle has area 12, find the area of the larger triangle.
75
Find the measure of each interior angle of a regular decagon.
144 degrees
Triangle ABC has sides 13, 14, 15. Find the area of triangle ABC.
84
From a point outside a circle, two tangents are drawn. The distance from the point to the center of the circle is 26, and the radius is 10. Find the length of each tangent.
Two similar triangles have perimeters 24 and 36. The area of the smaller triangle is 16. Find the area of the larger triangle.
36
The sum of the interior angles of a convex polygon is 1980. How many sides does the polygon have?
13
A regular hexagon is inscribed in an equilateral triangle so that each vertex of the hexagon lies on a different side of the triangle, and each side of the hexagon is parallel to a side of the triangle. The side length of the equilateral triangle is 12. Find the area of the hexagon.
36 * root(3)
Triangle ABC has side lengths 13, 14, 15. Let R be the circumradius of triangle ABC. A circle with radius R is drawn. Find the area of triangle ABC divided by the area of its circumcircle.
21 / 4(pi)
In triangle ABC, point D lies on BC such that AD is the angle bisector of ∠A. Suppose AB=10, AC=14, and BD=5. Find the length of DC.
7
A circle and a square are drawn with some overlapping area.
The area inside the square but outside the circle is EQUAL to the area inside the circle but outside the square. If the square has a side length of 4, what is the area of the circle?
4 * root(pi) / pi