MathDB
Prove angle is right

Source: All-Russian 2011

May 17, 2011
geometrygeometry proposed

Problem Statement

Given is an acute triangle ABCABC. Its heights BB1BB_1 and CC1CC_1 are extended past points B1B_1 and C1C_1. On these extensions, points PP and QQ are chosen, such that angle PAQPAQ is right. Let AFAF be a height of triangle APQAPQ. Prove that angle BFCBFC is a right angle.