1)In the diagram below, we have angle PQR = angle PRQ = angle STR = angle RST, QR = 8, and QS = 2. Find PQ.
2)In triangle ABC, AB = 3, BC = 4, and angle B = 90 degrees. Square DEFG is inscribed in triangle ABC such that D and G are on side AC, E is on side AB, and F is on side BC. Find the side length of the square.
3) In triangle ABC, angle A = 30 degrees and angle B = 60 degrees. Point X is on side AC such that line segment BX bisects angle ABC. If AB = 12, then find the area of triangle BXA.
4) Points A, B, and C are on sides WX, YZ, and XY of rectangle WXYZ as shown below such that XA = 4, YB = 18, angle ACB= 90 degrees, and YC = 2XC. Find AB.