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area of PKQI is half the area of ABC, incircle related

Source: Tuymaada Junior 2005 p2

May 12, 2019
geometryareasarea of a triangle

Problem Statement

Points X X and Y Y are the midpoints of the sides AB AB and AC AC of the triangle ABC ABC , I I is the center of its inscribed circle, K K is the point of tangency of the inscribed circles with side BC BC . The external angle bisector at the vertex B B intersects the line XY XY at the point P P , and the external angle bisector at the vertex of C C intersects XY XY at Q Q . Prove that the area of the quadrilateral PKQI PKQI is equal to half the area of the triangle ABC ABC .
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