MathDB
Isoceles triangle, cyclic quadrilateral

Source: BMO 2018 Shortlist G6

May 4, 2019
geometrycircumcircleparallelogramcyclic quadrilateralmoving points

Problem Statement

In a triangle ABCABC with AB=ACAB=AC, ω\omega is the circumcircle and OO its center. Let DD be a point on the extension of BABA beyond AA. The circumcircle ω1\omega_{1} of triangle OADOAD intersects the line ACAC and the circle ω\omega again at points EE and GG, respectively. Point HH is such that DAEHDAEH is a parallelogram. Line EHEH meets circle ω1\omega_{1} again at point JJ. The line through GG perpendicular to GBGB meets ω1\omega_{1} again at point NN and the line through GG perpendicular to GJGJ meets ω\omega again at point LL. Prove that the points L,N,H,GL, N, H, G lie on a circle.
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