ILL 1985 Problem 55

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 $MT_1$ and $MT_2$ be tangents to the circle with center $A$ and radius $AB$ . Determine the locus of the orthocenter of the triangle $MT_1T_2.$