P10

Part of 2015 Sharygin Geometry Olympiad

Problems(1)

convex quadrilateral divided into 4 similar triangles by diagonals is tangential

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P10

The diagonals of a convex quadrilateral divide it into four similar triangles. Prove that is possible to inscribe a circle into this quadrilateral

geometrysimilar trianglestangential quadrilateral