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A is the incenter if the centers of circles aren't collinear

Source: Turkey National Olympiad 2002 - D1 - P2

March 11, 2011
geometryincentercircumcircleangle bisectorgeometry unsolved

Problem Statement

Two circles are externally tangent to each other at a point AA and internally tangent to a third circle Γ\Gamma at points BB and C.C. Let DD be the midpoint of the secant of Γ\Gamma which is tangent to the smaller circles at A.A. Show that AA is the incenter of the triangle BCDBCD if the centers of the circles are not collinear.
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