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AP is tangent to the circumcircle of BLP, starting with a right triangle

Source: Ukrainian Geometry Olympiad 2017 X p3

December 12, 2018
geometrycircumcircletangentright triangle

Problem Statement

On the hypotenuse ABAB of a right triangle ABCABC, we denote a point KK such that BK=BCBK = BC. Let PP be a point on the perpendicular from the point KK to line CKCK, equidistant from the points KK and BB. Let LL be the midpoint of CKCK. Prove that line APAP is tangent to the circumcircle of ΔBLP\Delta BLP.
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