MathDB
ABC is similar to XYZ

Source: China TST 2011 - Quiz 2 - D2 - P1

May 20, 2011
geometrycircumcirclegeometric transformationreflectionperpendicular bisector

Problem Statement

Let AA′,BB′,CC′AA',BB',CC' be three diameters of the circumcircle of an acute triangle ABCABC. Let PP be an arbitrary point in the interior of △ABC\triangle ABC, and let D,E,FD,E,F be the orthogonal projection of PP on BC,CA,ABBC,CA,AB, respectively. Let XX be the point such that DD is the midpoint of A′XA'X, let YY be the point such that EE is the midpoint of B′YB'Y, and similarly let ZZ be the point such that FF is the midpoint of C′ZC'Z. Prove that triangle XYZXYZ is similar to triangle ABCABC.
Back to ProblemsView on AoPS