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Geometry Mathley 10.3 2 lines and a circle concurrent

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June 7, 2020
concurrentgeometrycircumcircle

Problem Statement

Let ABCABC be a triangle inscribed in a circle (O)(O). d is the tangent at AA of (O),P(O), P is an arbitrary point in the plane. D,E,FD,E, F are the projections of PP on BC,CA,ABBC,CA,AB. Let DE,DFDE,DF intersect the line dd at M,NM,N respectively. The circumcircle of triangle DEFDEF meets CA,ABCA,AB at K,LK,L distinct from E,FE, F. Prove that KNKN meets LMLM at a point on the circumcircle of triangle DEFDEF.
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