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at least 1 of the feet of altitudes in 4 triangles of convex quadr. lies on side

Source: Mexican Mathematical Olympiad 1994 OMM P5

July 29, 2018
geometryconvex quadrilateralaltitudes

Problem Statement

ABCDABCD is a convex quadrilateral. Take the 1212 points which are the feet of the altitudes in the triangles ABC,BCD,CDA,DABABC, BCD, CDA, DAB. Show that at least one of these points must lie on the sides of ABCDABCD.
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