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angle bisector _|_ AB, #, bisectors (2016 Novosibirsk Oral Geo Oly 8-9 p5)

Source:

April 26, 2021

geometryparallelogramperpendicular

Problem Statement

In the parallelogram

CMNP

extend the bisectors of angles

MCN

and

PCN

and intersect with extensions of sides PN and

MN

at points

A

and

B

, respectively. Prove that the bisector of the original angle

C

of the the parallelogram is perpendicular to

AB

. https://cdn.artofproblemsolving.com/attachments/f/3/fde8ef133758e06b1faf8bdd815056173f9233.png