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orthocenter

Source:

December 17, 2011
geometrycircumcirclefunctioncyclic quadrilateralgeometry unsolved

Problem Statement

Points A1,B1,C1A_1, B_1, C_1 inside an acute-angled triangle ABCABC are selected on the altitudes from A,B,CA, B, C respectively so that the sum of the areas of triangles ABC1,BCA1ABC_1, BCA_1, and CAB1CAB_1 is equal to the area of triangle ABCABC. Prove that the circumcircle of triangle A1B1C1A_1B_1C_1 passes through the orthocenter HH of triangle ABCABC.
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