MathDB
Planes pass through a common point [ Iran Second Round 1995]

Source:

November 25, 2010
geometrycircumcirclegeometry proposed

Problem Statement

In a quadrilateral ABCDABCD let A′,B′,C′A', B', C' and D′D' be the circumcenters of the triangles BCD,CDA,DABBCD, CDA, DAB and ABCABC, respectively. Denote by S(X,YZ)S(X, YZ) the plane which passes through the point XX and is perpendicular to the line YZ.YZ. Prove that if A′,B′,C′A', B', C' and D′D' don't lie in a plane, then four planes S(A,C′D′),S(B,A′D′),S(C,A′B′)S(A, C'D'), S(B, A'D'), S(C, A'B') and S(D,B′C′)S(D, B'C') pass through a common point.
Back to ProblemsView on AoPS