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locus of point with equal angles

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March 7, 2007
geometrycircumcirclegeometry unsolved

Problem Statement

A point PP is given inside an acute-angled triangle ABCABC. Let A′,B′,C′A',B',C' be the orthogonal projections of PP on sides BC,CA,ABBC, CA, AB respectively. Determine the locus of points PP for which ∠BAC=∠B′A′C′\angle BAC = \angle B'A'C' and ∠CBA=∠C′B′A′\angle CBA = \angle C'B'A'
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