MathDB

6

Part of 2004 South East Mathematical Olympiad

Problems(1)

an isosceles triangle problem

Source: China south east mathematical olympiad 2004 day2 problem 6

6/29/2013
ABC is an isosceles triangle with AB=AC. Point D lies on side BC. Point F is inside △\triangleABC and lies on the circumcircle of triangle ADC. The circumcircle of triangle BDF intersects side AB at point E. Prove that CD⋅EF+DF⋅AE=BD⋅AFCD\cdot EF+DF\cdot AE=BD\cdot AF.
geometrycircumcircletrigonometrycyclic quadrilateralgeometry unsolved