MathDB
right angle wanted - 2005 Cuba MO 2.5

Source:

September 15, 2024
geometryright angleperpendicular

Problem Statement

On the circumcircle of triangle ABCABC, point PP is taken in such a way that the perpendicular drawn by the point PP to the line ACAC cuts the circle also at the point QQ, the perpendicular drawn by the point QQ to the line ABAB cuts the circle also at point R and the perpendicular drawn by point RR to the line BC cuts the circle also at the point PP. Let OO be the center of this circle. Prove that POC=90o\angle POC = 90^o .