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The South African Mathematical Olympiad 2007

Source: Problem 4

August 22, 2008
geometrygeometry proposed

Problem Statement

Let ABC ABC be a triangle and PQRS PQRS a square with P P on AB AB, Q Q on AC AC, and R R and S S on BC BC. Let H H on BC BC such that AH AH is the altitude of the triangle from A A to base BC BC. Prove that: (a) \frac{1}{AH} \plus{}\frac{1}{BC}\equal{}\frac{1}{PQ} (b) the area of ABC ABC is twice the area of PQRS PQRS iff AH\equal{}BC
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