MathDB
Circles and lines

Source: JBMO Shortlist 2006

November 10, 2008
geometry proposedgeometry

Problem Statement

Circles C1 \mathcal{C}_1 and C2 \mathcal{C}_2 intersect at A A and B B. Let MAB M\in AB. A line through M M (different from AB AB) cuts circles C1 \mathcal{C}_1 and C2 \mathcal{C}_2 at Z,D,E,C Z,D,E,C respectively such that D,EZC D,E\in ZC. Perpendiculars at B B to the lines EB,ZB EB,ZB and AD AD respectively cut circle C2 \mathcal{C}_2 in F,K F,K and N N. Prove that KF\equal{}NC.