IMO 1986 LL USS79

Let AA1, BB1, CC1 be the altitudes in an acute-angled triangle

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IMO 1986 LL USS79

Origin: USS

Problem

Let AA1, BB1, CC1 be the altitudes in an acute-angled triangle ABC. K and M are points on the line segments A1C1 and B1C1 respec- tively. Prove that if the angles MAK and CAA1 are equal, then the angle C1KM is bisected by AK.