MathDB
weird square( 2023 HMMT G5)

Source:

February 21, 2023
HMMT

Problem Statement

Let ABCABC be a triangle with AB=13,BC=14,AB = 13, BC = 14, andCA=15 CA = 15. Suppose PQRSPQRS is a square such that PP and RR lie on line BC,QBC, Q lies on line CACA, and SS lies on line ABAB. Compute the side length of this square.