MathDB

Angel Bisector and Equilateral Pentagon AMNPQ

Source: 2016 USAMO 5

April 20, 2016

geometry

Problem Statement

An equilateral pentagon

AMNPQ

is inscribed in triangle

ABC

such that

M\in\overline{AB}

,

Q\in\overline{AC}

, and

N,P\in\overline{BC}

. Let

S

be the intersection of

\overleftrightarrow{MN}

and

\overleftrightarrow{PQ}

. Denote by

\ell

the angle bisector of

\angle MSQ

.
Prove that

\overline{OI}

is parallel to

\ell

, where

O

is the circumcenter of triangle

ABC

, and

I

is the incenter of triangle

ABC

.

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