MathDB

2

Part of 2003 Mexico National Olympiad

Problems(1)

three circles

Source: Mexico 2003

3/2/2007
A,B,CA, B, C are collinear with BB betweeen AA and CC. K1K_{1} is the circle with diameter ABAB, and K2K_{2} is the circle with diameter BCBC. Another circle touches ACAC at BB and meets K1K_{1} again at PP and K2K_{2} again at QQ. The line PQPQ meets K1K_{1} again at RR and K2K_{2} again at SS. Show that the lines ARAR and CSCS meet on the perpendicular to ACAC at BB.
geometryparallelogrampower of a pointradical axisgeometry unsolved