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points are collinear, lying on a line parallel to a given one

Source: Greece JBMO TST 2011 p4

April 29, 2019
geometrycircumcirclecollinearcircles

Problem Statement

Let ABCABC be an acute and scalene triangle with AB<ACAB<AC, inscribed in a circle c(O,R)c(O,R) (with center OO and radius RR). Circle c1(A,AB)c_1(A,AB) intersects side BCBC at point EE and circle cc at point FF. EFEF intersects for the second time circle cc at point DD and side ACAC at point MM. ADAD intersects BCBC at point KK. Circumcircle of triangle BKDBKD intersects ABAB at point LL . Prove that points K,L,MK,L,M lie on a line parallel to BFBF.
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