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EF=diameter of circumcircle of AO_1O_2 (2017 Kyiv City MO Round2 10.3)

Source:

September 10, 2020

geometrycircumcirclediametercircles

Problem Statement

Circles

w_1

and

w_2

with centers at points

O_1

and

O_2

respectively, intersect at points

A

and

B

. A line passing through point

B

, intersects the circles

w_1

and

w_2

at points

C

and

D

other than

B

. Tangents to the circles

w_1

and

w_2

at points

C

and

D

intersect at point

E

. Line

EA

intersects the circumscribed circle

w

of triangle

AO_1O_2

at point

F

. Prove that the length of the segment is

EF

is equal to the diameter of the circle

w

.
(Vovchenko V., Plotnikov M.)

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