MathDB

2

Part of 1998 Argentina National Olympiad

Problems(1)

quadrilateral of orthocenters is a parallelogram

Source: 1998 Argentina OMA L3 p2

6/11/2020
Let a quadrilateral ABCDABCD have an inscribed circle and let K,L,M,NK, L, M, N be the tangency points of the sides AB,BC,CDAB, BC, CD and DADA, respectively. Consider the orthocenters of each of the triangles △AKN,△BLK,△CML\vartriangle AKN, \vartriangle BLK, \vartriangle CML and △DNM\vartriangle DNM. Prove that these four points are the vertices of a parallelogram.
geometryorthocentertangential quadrilateralparallelogram