You are given a circle with diameter AB and a point C. You are to construct a perpendicular CD to the diameter AB using only a straight edge (a ruler without markings).
In trapezoid ABCD, the sides AB and CD are parallel and AB > CD. Point P is in the interior, dividing the trapezoid into 4 triangles with areas CPD = 2, CPB = 3, BPA = 4, APD = 5. What is AB/CD equal to?
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?
Triangle ABC is inscribed in a circle. Construct chord AD and let E be the intersection of chords AD and BC. If AB = AC = 12 and AE = 8, then what is the length of AD?
A circle has two non-intersecting chords AB and CD. Chord RS intersects chord AB at P and CD at Q. If AP = 12, BP = 20, CQ = 10, DQ = 24, and PQ = 14, what is the length of chord RS?
Construct a circle of radius 1. From a point on the circle, construct another circle of radius 1. Inscribe a square where the two circles overlap. What is the area of the square?
