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perpendicular wanted, intersecting circles related

Source: 2015 Grand Duchy of Lithuania, Mathematical Contest p2 (Baltic Way TST)

October 3, 2020

geometryperpendicularcircles

Problem Statement

Let

\omega_1

and

\omega_2

be two circles , with respective centres

O_1

and

O_2

, that intersect each other in

A

and

B

. The line

O_1A

intersects

\omega_2

in

A

and

C

and the line

O_2A

inetersects

\omega_1

in

A

and

D

. The line through

B

parallel to

AD

intersects

\omega_1

in

B

and

E

. Suppose that

O_1A

is parallel to

DE

. Show that

CD

is perpendicular to

O_2C

.

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