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square inside a square, AE = BF = CG = DH - 2019 Ecuador Juniors (OMEC) L2 p4

Source:

October 24, 2022

geometrysquare

Problem Statement

Let

ABCD

be a square. On the segments

AE = BF = CG = DH

,

BC

,

CD

and

DA

, choose points

E, F, G

and

H

, respectively, such that

AE = BF = CG = DH

. Let

P

be the intersection point of

AF

and

DE

,

Q

be the intersection point of

BG

and

AF

,

R

the intersection point of

CH

and

BG

, and

S

the point of intersection of

DE

and

CH

. Prove that

PQRS

is a square.

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