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Three circles have a common point

Source: Swiss Math Olympiad 2010 - final round, problem 9

March 16, 2010

geometrycircumcirclepower of a pointradical axisgeometry proposed

Problem Statement

Let

k

and

k'

two concentric circles centered at

O

, with

k'

being larger than

k

. A line through

O

intersects

k

at

A

and

k'

at

B

such that

O

seperates

A

and

B

. Another line through

O

intersects

k

at

E

and

k'

at

F

such that

E

separates

O

and

F

. Show that the circumcircle of

\triangle{OAE}

and the circles with diametres

AB

and

EF

have a common point.

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