MathDB
MX passes through fixed point

Source: Iran RMM TST 2019,day2 p6

July 30, 2019
geometry

Problem Statement

Let ABCDABCD be cyclic quadrilateral with circumcircle ω\omega and MM be any point on ω\omega .\\ Let EE and FF be the intersection of AB,CDAB,CD and AD,BCAD,BC respectively.\\ MEME intersects lines AD,BCAD,BC at P,QP,Q and similarly MFMF intersects lines AB,CDAB,CD at R,SR,S .\\ Let the lines PSPS and RQRQ meet at XX .\\ Prove that as MM varies over ω\omega \\ MXMX passes through fixed point.\\
Proposed by Mehdi Etesami Fard
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