PF is perpendicular to AB if ON + OH = BK
Source: 1998 Belarus TST 6.1
June 9, 2020
geometryperpendicular bisectorangle bisectormidpointsangle
Problem Statement
Let be a point inside an acute angle with the vertex and be the feet of the perpendiculars drawn from onto the sides of the angle. Let point belong to the bisector of the angle, be the foot of the perpendicular from onto either side of the angle. Denote by the midpoints of the segments respectively. Known that , prove that is perpendicular to .Ya. Konstantinovski