Ken's POTW

Bisection in a Triangle
The circle inscribed in the triangle ABC touches the side AC in the point K. Let the center of the circle be O, and the midpoint of AC be D. Prove that the line connecting O with D bisects the BK segment.

Source: Submitted by reader Phillippe Fondanaiche, citing W. PERTSEL ( The problems of the All-Soviet-Union mathematical competitions 1961-1987, #112 )

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