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IMO ShortList 1999, geometry problem 5

Source: IMO ShortList 1999, geometry problem 5

November 13, 2004

geometryIMO Shortlist

Problem Statement

Let

ABC

be a triangle,

\Omega

its incircle and

\Omega_{a}, \Omega_{b}, \Omega_{c}

three circles orthogonal to

\Omega

passing through

(B,C),(A,C)

and

(A,B)

respectively. The circles

\Omega_{a}

and

\Omega_{b}

meet again in

C'

; in the same way we obtain the points

B'

and

A'

. Prove that the radius of the circumcircle of

A'B'C'

is half the radius of

\Omega

.

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