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DE _|_ OC, interssecting circles

Source: - All-Russian MO 1998 Regional (R4) 11.2

September 17, 2024

perpendiculargeometry

Problem Statement

Circle

S

with center

O

and circle

S'

intersect at points

A

and

B

. Point

A

is taken on the arc of a circle

B

lying inside

E

. Denote the intersection points of

AC

and

BC

with

S'

, other than

A

and

B

, as

E

and

D

, respectively. Prove that lines

DE

and

OC

are perpendicular.

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