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computational for juniors in Tuymaada , tangent circle given

Source: Tuymaada Olympiad 2019 juniors p7

July 22, 2019
geometrytangentcircle

Problem Statement

A circle ω\omega touches the sides AAB and BCBC of a triangle ABCABC and intersects its side ACAC at KK. It is known that the tangent to ω\omega at KK is symmetrical to the line ACAC with respect to the line BKBK. What can be the difference AK−CKAK -CK if AB=9AB = 9 and BC=11BC = 11?
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