MathDB

Conditional geo with centroid

Source: Singapore Open MO Round 2 2023 P1

July 1, 2023

geometry

Problem Statement

In a scalene triangle

ABC

with centroid

G

and circumcircle

\omega

centred at

O

, the extension of

AG

meets

\omega

at

M

; lines

AB

and

CM

intersect at

P

; and lines

AC

and

BM

intersect at

Q

. Suppose the circumcentre

S

of the triangle

APQ

lies on

\omega

and

A, O, S

are collinear. Prove that

\angle AGO = 90^{o}

.

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