Geometry · Exterior angle bisector · Midline · Isosceles triangle · Right angle in semicircle
Let \(M\) and \(P\) be the feet of the perpendiculars from the vertex \(A\) of a triangle \(ABC\) to the bisectors of the exterior angles at the vertices \(B\) and \(C\), respectively. Prove that the length of the segment \(MP\) is equal to half the perimeter of the triangle \(ABC\).
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Serbian Municipal Competition 2011, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source