MathDB

2

Part of 1975 Poland - Second Round

Problems(1)

if 2 quads are tangential, so is a third one

Source: Polish MO Second Round 1975 p2

9/8/2024
In the convex quadrilateral ABCD ABCD , the corresponding points M M and N N are chosen on the adjacent sides AB‾ \overline{AB} and BC‾ \overline{BC} and the intersection point of the segments AN AN and GM GM is marked by 0. Prove that if circles can be inscribed in the quadrilaterals AOCD AOCD and BMON BMON , then a circle can also be inscribed in the quadrilateral ABCD ABCD .
geometrytangential quadrilateraltangential