MathDB

ABCD square wanted, 3 circles (O,OA), (A,AO), (P,PQ)

Source: Mathematics Regional Olympiad of Mexico Center Zone 2020 P4

November 14, 2021

squaregeometrycircles

Problem Statement

Let

\Gamma_1

be a circle with center

O

and

A

a point on it. Consider the circle

\Gamma_2

with center at

A

and radius

AO

. Let

P

and

Q

be the intersection points of

\Gamma_1

and

\Gamma_2

. Consider the circle

\Gamma_3

with center at

P

and radius

PQ

. Let

C

be the second intersection point of

\Gamma_3

and

\Gamma_1

. The line

OP

cuts

\Gamma_3

at

R

and

S

, with

R

outside

\Gamma_1

.

RC

cuts

\Gamma_1

into

B

.

CS

cuts

\Gamma_1

into

D

. Show that

ABCD

is a square.

Back to Problems View on AoPS