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Two triangles

Source: Turkey TST 2007

April 10, 2007
geometrycircumcircleanalytic geometrytrigonometrygeometry proposed

Problem Statement

Let ABCABC is an acute angled triangle and let A1, B1, C1A_{1},\, B_{1},\, C_{1} are points respectively on BC, CA, ABBC,\,CA,\,AB such that △ABC\triangle ABC is similar to △A1B1C1.\triangle A_{1}B_{1}C_{1}. Prove that orthocenter of A1B1C1A_{1}B_{1}C_{1} coincides with circumcenter of ABCABC.
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