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Romania Junior TST 2021 Day 3 P2

Source:

June 7, 2021

geometryromaniaRomanian TST

Problem Statement

Let

O

be the circumcenter of triangle

ABC

and let

AD

be the height from

A

(

D\in BC

). Let

M,N,P

and

Q

be the midpoints of

AB,AC,BD

and

CD

respectively. Let

\mathcal{C}_1

and

\mathcal{C}_2

be the circumcircles of triangles

AMN

and

POQ

. Prove that

\mathcal{C}_1\cap \mathcal{C}_2\cap AD\neq \emptyset

.

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