41st Swedish 2001 Problem 4 ABC is a triangle. A circle through A touches the side BC at D and intersects the sides AB and AC again at E, F respectively. EF bisects ∠AFD and ∠ADC = 80 o . Find ∠ABC.
∠AFD = ∠ADB = 100 o , so ∠DFE = 50 o . Hence ∠DAE = 50 o . Hence ∠B = 180 o - 100 o - 50 o = 30 o . 41st Swedish 2001 © John Scholes jscholes@kalva.demon.co.uk 18 January 2004 Last corrected/updated 18 Jan 04