MathDB

3

Part of 2022 Centroamerican and Caribbean Math Olympiad

Problems(1)

cyclic quadrilateral with orthocenter and circumcenter

Source: 2022 Centroamerican and Caribbean Mathematical Olympiad, P3

12/1/2022
Let ABCABC an acutangle triangle with orthocenter HH and circumcenter OO. Let DD the intersection of AOAO and BHBH. Let PP be the point on ABAB such that PH=PDPH=PD. Prove that the points B,D,OB, D, O and PP lie on a circle.
geometrycircumcircleorthocentercyclic quadrilateral