MathDB
2011 PUMaC Geometry A2 / B6

Source:

September 24, 2019
geometry

Problem Statement

A rectangular piece of paper has corners labeled A,B,CA, B, C, and DD, with BC=80BC = 80 and CD=120CD = 120. Let MM be the midpoint of side ABAB. The corner labeled AA is folded along line MDMD and the corner labeled BB is folded along line MCMC until the segments AMAM and MBMB coincide. Let SS denote the point in space where AA and BB meet. If HH is the foot of the perpendicular from SS to the original plane of the paper, find HMHM.