The diagram shows a sphere with center O that contains a cone whose diameter AB is equal to its height CM. What is the ratio of the cone’s volume to the sphere’s volume?
A right triangle ABC has legs AB = 4, BC = 6, and has a semicircle O with its center on the hypotenuse tangent to the legs AB at D and BC at E. What is the radius of the semicircle?
In triangleABC, side AB = 20, AC = 11, and BC = 13. Find the diameter of the semicircle inscribed in ABC, whose diameter lies on AB, and that is tangent to AC and BC.
A circle has diameter AB. A line starts at A and zig-zags exactly 4 times between the diameter and the circumference until it ends at B, as shown below.
If each of the angles the line makes with the diameter has the same measure α, what is α equal to?
