MathDB

2013.8.5

Part of Kyiv City MO Juniors 2003+ geometry

Problems(1)

4 incircles in convex ABCD concurrent if ABCD is rhombus (2013 Kyiv City MO 8.5)

Source:

8/4/2020
Let ABCDABCD be a convex quadrilateral. Prove that the circles inscribed in the triangles ABCABC, BCDBCD, CDACDA and DABDAB have a common point if and only if ABCDABCD is a rhombus.
geometryrhombusconcurrentcirclesconcurrency