MathDB
Interior tracing

Source: USAMO 1991

October 27, 2005
geometrygeometry solved

Problem Statement

Let  D \, D \, be an arbitrary point on side  AB \, AB \, of a given triangle  ABC, \, ABC, \, and let  E \, E \, be the interior point where  CD \, CD \, intersects the external common tangent to the incircles of triangles  ACD \, ACD \, and  BCD\, BCD. As  D \, D \, assumes all positions between  A \, A \, and  B \, B \,, prove that the point  E \, E \, traces the arc of a circle.
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