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        riddles >> medium >> Proof of concurrence
        
(Message started by: Ronno on Apr 8^th, 2010, 9:13pm)

Title: Proof of concurrence
Post by Ronno on Apr 8^th, 2010, 9:13pm

Let ABC be a triangle with circumcenter O and incenter I such that O is different from I. Let AK, BL, CM be the altitudes of ABC; let U, V, W be the midpoints of AK, BL, CM respectively. Let D, E, F be the points at which the incircle of ABC touches the sides BC, CA, AB. Prove that UD, VE, WF and OI are concurrent.