MathDB

6

Part of 1989 Poland - Second Round

Problems(1)

two tangential quads leadto a third tangential quad

Source: Polish MO Recond Round 1989 p6

9/9/2024
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 .
geometrytangential