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3 circles, incircle, circle tangent to incircle passing through BC, A- excircle

Source: SRMC 2007

September 2, 2018
geometryincircletangent circlesexcircle

Problem Statement

Let ω\omega be the incircle of triangle ABCABC touches BCBC at point KK . Draw a circle passing through points BB and CC , and touching ω\omega at the point SS . Prove that SKS K passes through the center of the exscribed circle of triangle ABCA B C , tangent to side BCB C .
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