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the centers of the excircles of a triangle ABC

Source: Russian Olympiad 2004, problem 11.2

May 4, 2004

geometrycircumcircleEulertrapezoidincenterrectanglegeometric transformation

Problem Statement

Let

I(A)

and

I(B)

be the centers of the excircles of a triangle

ABC,

which touches the sides

BC

and

CA

in its interior. Furthermore let

P

a point on the circumcircle

\omega

of the triangle

ABC.

Show that the center of the segment which connects the circumcenters of the triangles

I(A)CP

and

I(B)CP

coincides with the center of the circle

\omega.