The vertices of a right triangle ABC inscribed in a circle divide the circumference into three arcs. The right angle is at A, so that the opposite arc BC is a semicircle while arc BC and arc AC are supplementary. To each of three arcs, we draw a tangent such that its point of tangency is the mid point of that portion of the tangent intercepted by the extended lines AB,AC. More precisely, the point D on arc BC is the midpoint of the segment joining the points D′ and D′′ where tangent at D intersects the extended lines AB,AC. Similarly for E on arc AC and F on arc AB. Prove that triangle DEF is equilateral. geometry proposedgeometry