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two tangential quads leadto a third tangential quad

Source: Polish MO Recond Round 1989 p6

September 9, 2024
geometrytangential

Problem Statement

In the triangle ABC ABC , the lines CP CP , AP AP , BP BP are drawn through the internal point P P and intersect the sides AB AB , BC BC , CA CA at points K K , L L , M M, respectively. Prove that if circles can be inscribed in the quadrilaterals AKPM AKPM and KBLP KBLP , then a circle can also be inscribed in the quadrilateral LCMP LCMP .
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