IMO 1985 LL MOR55

The points A, B, C are in this order on line D, and AB = 4BC.

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IMO 1985 LL MOR55

Origin: MOR

Problem

The points A, B, C are in this order on line D, and AB = 4BC. Let M be a variable point on the perpendicular to D through C. Let MT1 and MT2 be tangents to the circle with center A and radius AB. Determine the locus of the orthocenter of the triangle MT1T2.