MathDB

2

Part of 2016 EGMO

Problems(1)

Tangent Line.

Source: EGMO 2016 Day 1 Problem 2

4/12/2016
Let ABCDABCD be a cyclic quadrilateral, and let diagonals ACAC and BDBD intersect at XX.Let C1,D1C_1,D_1 and MM be the midpoints of segments CX,DXCX,DX and CDCD, respecctively. Lines AD1AD_1 and BC1BC_1 intersect at YY, and line MYMY intersects diagonals ACAC and BDBD at different points EE and FF, respectively. Prove that line XYXY is tangent to the circle through E,FE,F and XX.
geometrycyclic quadrilateraltangentmidpointsEGMOEGMO 2016