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intersection point of 2 perpendiculars lies on a medial line

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P19

August 2, 2018
geometryconcurrent

Problem Statement

Let LL and KK be the feet of the internal and the external bisector of angle AA of a triangle ABCABC. Let PP be the common point of the tangents to the circumcircle of the triangle at BB and CC. The perpendicular from LL to BCBC meets APAP at point QQ. Prove that QQ lies on the medial line of triangle LKPLKP.
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