MathDB

Regular Pentagon

Source: Austrian Mathematical Olympiad 2017

May 2, 2018

geometry

Problem Statement

Let

ABCDE

be a regular pentagon with center

M

. A point

P

(different from

M

) is chosen on the line segment

MD

. The circumcircle of

ABP

intersects the line segment

AE

in

A

and

Q

and the line through

P

perpendicular to

CD

in

P

and

R

. Prove that

AR

and

QR

have same length.
proposed by Stephan Wagner

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