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Circumcircle of medial triangle

Source: KJMO 2017 p6

July 26, 2019
geometrycircumcircleKJMO

Problem Statement

Let triangle ABCABC be an acute scalene triangle, and denote D,E,FD,E,F by the midpoints of BC,CA,ABBC,CA,AB, respectively. Let the circumcircle of DEFDEF be O1O_1, and its center be NN. Let the circumcircle of BCNBCN be O2O_2. O1O_1 and O2O_2 meet at two points P,QP, Q. O2O_2 meets ABAB at point K(≠B)K(\neq B) and meets ACAC at point L(≠C)L(\neq C). Show that the three lines EF,PQ,KLEF,PQ,KL are concurrent.
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