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