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Segment is bisected by the NPC

Source: Oral Moscow geometry olympiad 8-9.3

April 20, 2023

geometry

Problem Statement

Given is a triangle

ABC

and

M

is the midpoint of the minor arc

BC

. Let

M_1

be the reflection of

M

with respect to side

BC

. Prove that the nine-point circle bisects

AM_1

.

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