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locus in a TST, starting with incircle of isosceles

Source: Ukraine TST 2012 p4

April 29, 2020
geometryLocusincircleisosceles

Problem Statement

Given an isosceles triangle ABCABC (AB=ACAB = AC), the inscribed circle ω\omega touches its sides ABAB and ACAC at points KK and LL, respectively. On the extension of the side of the base BCBC, towards BB, an arbitrary point MM. is chosen. Line MM intersects ω\omega at the point NN for the second time, line BNBN intersects the second point ω\omega at the point PP. On the line PKPK, there is a point XX such that KK lies between PP and XX and KX=KMKX = KM. Determine the locus of the point XX.
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