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JBMO TST Bosnia and Herzegovina 2020 P3

Source:

August 10, 2020
geometryangle bisector

Problem Statement

The angle bisector of ∠ABC\angle ABC of triangle ABCABC (AB>BCAB>BC) cuts the circumcircle of that triangle in KK. The foot of the perpendicular from KK to ABAB is NN, and PP is the midpoint of BNBN. The line through PP parallel to BCBC cuts line BKBK in TT. Prove that the line NTNT passes through the midpoint of ACAC.
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