MathDB
Tangent line to the circumcircle

Source: 239 2012 J5

July 30, 2020
geometrycircumcircle

Problem Statement

On the hypotenuse ABAB of the right-angled triangle ABCABC, a point KK is chosen such that BK=BCBK = BC. Let PP be a point on the perpendicular line from point KK to the line CKCK, equidistant from the points KK and BB. Also let LL denote the midpoint of the segment CKCK. Prove that line APAP is tangent to the circumcircle of the triangle BLPBLP.