MathDB

17

Part of 2005 Postal Coaching

Problems(1)

excircles touch corresponding sides of triangle ABC

Source: ARO 2005 - problem 11.3

4/30/2005
Let A′, B′, C′A',\,B',\,C' be points, in which excircles touch corresponding sides of triangle ABCABC. Circumcircles of triangles A′B′C, AB′C′, A′BC′A'B'C,\,AB'C',\,A'BC' intersect a circumcircle of ABCABC in points C1≠C, A1≠A, B1≠BC_1\ne C,\,A_1\ne A,\,B_1\ne B respectively. Prove that a triangle A1B1C1A_1B_1C_1 is similar to a triangle, formed by points, in which incircle of ABCABC touches its sides.
geometrycircumcirclegeometry solved