MathDB

Concurrency geometry

Source: Kvant Magazine No. 9 2023 M2764

January 9, 2024

geometryconcurrency

Problem Statement

Let

BE{}

and

CF

be heights in the acute-angled triangle

ABC{}

and let

O{}

be its circumcenter. The points

M{}

and

P{}

are selected on the side

CF{}

so that

(NCE)

The line

BE{}

intersects the circle

(MBF)

a second time at

P{}

and the line

CF{}

intersects the circle

(NCE)

a second time at

Q.{}

Prove that the lines

PF, QE

and

AO{}

intersect at the same point.
Proposed by Luu Dong

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