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Parallel and three circles

Source: Iran 2nd round 2012-Day1-P1

April 30, 2012

geometryincentergeometric transformationgeometry proposed

Problem Statement

Consider a circle

C_1

and a point

O

on it. Circle

C_2

with center

O

, intersects

C_1

in two points

P

and

Q

.

C_3

is a circle which is externally tangent to

X

at

R

and internally tangent to

C_1

at

S

and suppose that

RS

passes through

Q

. Suppose

X

and

Y

are second intersection points of

PR

and

OR

with

C_1

. Prove that

QX

is parallel with

SY

.

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