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Serbia JBMO TST 2021 problem 4

Source: Serbia JBMO TST 2021

January 3, 2022

geometryorthocenterparallelogramCircumcentercircumcircle

Problem Statement

On sides

AB

and

AC

of an acute triangle

\Delta ABC

, with orthocenter

H

and circumcenter

O

, are given points

P

and

Q

respectively such that

APHQ

is a parallelogram. Prove the following equality: \begin{align*} \frac{PB\cdot PQ}{QA\cdot QO}=2 \end{align*}