Equal angles in the pentagon and perpendicular lines
Source: Polish MO 2008 Second Round (1st day)
February 22, 2008
geometrygeometric transformationreflectiongeometry proposed
Problem Statement
In the convex pentagon following equalities holds: \angle ABD\equal{} \angle ACE, \angle ACB\equal{}\angle ACD, \angle ADC\equal{}\angle ADE and \angle ADB\equal{}\angle AEC. The point is the intersection of the segments and . Prove that lines and are perpendicular.