MathDB

4

Part of 2004 South africa National Olympiad

Problems(1)

Isosceles triangles and tangent circles

Source: South African MO 2004 Q4

5/27/2012
Let A1A_1 and B1B_1 be two points on the base ABAB of isosceles triangle ABCABC (with C^>60∘\widehat{C}>60^\circ) such that A1CB1^=BAC^\widehat{A_1CB_1}=\widehat{BAC}. A circle externally tangent to the circumcircle of triangle △A1B1C\triangle A_1B_1C is tangent also to rays CACA and CBCB at points A2A_2 and B2B_2 respectively. Prove that A2B2=2ABA_2B_2=2AB.
geometrycircumcirclegeometry unsolved