MathDB

Invasion for the win

Source: Baltic Way 2021, Problem 14

November 15, 2021

geometrygeometry proposedcircumcircleCircumcentergeometry solvedHarmonic Quadrilateralsymmedian

Problem Statement

Let

ABC

be a triangle with circumcircle

\Gamma

and circumcentre

O

. Denote by

M

the midpoint of

BC

. The point

D

is the reflection of

A

over

BC

, and the point

E

is the intersection of

\Gamma

and the ray

MD

. Let

S

be the circumcentre of the triangle

ADE

. Prove that the points

A

,

E

,

M

,

O

, and

S

lie on the same circle.

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