XY_|_PO iff AP is angle bisector
Source: 2020 XXIII All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p11
May 4, 2021
perpendicularangle bisectorgeometryUkrainian TYM
Problem Statement
In the acute-angled triangle , the segment was drawn and the center was marked of the circumscribed circle. The circumcircle of triangle intersects the line for the second time at point , the circumcircle of the triangle intersects the line for the second time at the point . Prove that the lines and are perpendicular if and only if is the foor of the bisector of the triangle .