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Pentagon and lengths

Source: Sharygin 2019 Finals Day 2 Grade 8 P6

July 31, 2019

geometrySharygin Geometry Olympiad

Problem Statement

A point

H

lies on the side

AB

of regular polygon

ABCDE

. A circle with center

H

and radius

HE

meets the segments

DE

and

CD

at points

G

and

F

respectively. It is known that

DG=AH

. Prove that

CF=AH

.

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