In square ABCD, construct M along AB and N along BC. Then construct AN, DM, and CM. Let AN∩DM = P, AN∩CM = Q, and CM∩DM = R. If the area of PQRD = 1, what is the total area of APM + MQNB + NRC?
Triangle ABC has a right angle at B. Let Q be along BC and P be along AB such that AQ bisects angle A and CP bisects angle C. If AQ = 9 and CP = 8√2, what is the length of the hypotenuse AC?
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?
If ABCD is a square of area 1. E, F are mid points of AB and BC respectively. What is the area of blue region?
Suppose ABCD is an isosceles trapezoid with bases AB and CD and sides AD and BC such that |CD| > |AB|. Also suppose that |CD| = |AC| and that the altitude of the trapezoid is equal to |AB|
If |AB|/|CD| = a/b where a and b are positive coprime integers, then find a^b?
A triangle with sides AB = 3, BC = 4, and AC = 5 has an inscribed square PQRS with side QR along the side AC. What is the area of the square?
