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Euler Line parallel to A-tangent?

Source: India EGMO TST 2024/1

December 31, 2023

EulergeometryEgmo tstcircumcircle

Problem Statement

Let

NO = NA

be a triangle with circumcentre

O

and centroid

G

. Let

M

be the midpoint of

BC

and

N

the reflection of

M

across

O

. Prove that

NO = NA

if and only if

\angle AOG = 90^{\circ}

.
Proposed by Pranjal Srivastava

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