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common tangent of 3 circles wanted, mixtilinear circles related

Source: Mathley 2014.2 p4

August 20, 2020
geometrycommon tangentmixtilinear

Problem Statement

Let (O)(O) be the circumcircle of triangle ABCABC, and PP a point on the arc BCBC not containing AA. (Q)(Q) is the AA-mixtilinear circle of triangle ABCABC, and (K),(L)(K), (L) are the PP-mixtilinear circles of triangle PAB,PACPAB, PAC respectively. Prove that there is a line tangent to all the three circles (Q),(K)(Q), (K) and (L)(L).
Nguyen Van Linh, a student at Hanoi Foreign Trade University Cabinet
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