MathDB
rhombus, 4 equal incircles - 2015 Cuba 2.2

Source:

September 20, 2024
geometryrhombus

Problem Statement

Let ABCDABCD be a convex quadrilateral and let PP be the intersection of the diagonals ACAC and BDBD. The radii of the circles inscribed in the triangles △ABP\vartriangle ABP, △BCP\vartriangle BCP, △CDP\vartriangle CDP and △DAP\vartriangle DAP are the same. Prove that ABCDABCD is a rhombus,
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