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November 1st, 2019, 08:24 AM  #1 
Senior Member Joined: Mar 2015 From: Universe 2.71828i3.14159 Posts: 169 Thanks: 65 Math Focus: Area of Circle  Geometry Problem Series, Question 2:
$T$ is the middle point of the segment $AB$ of the convex quadrilateral $ABCD$. The circle $\omega$, through points $C,D,T$, is tangent to $AB$. $K$ and $L$ are the intersection points of $AD$ and $BC$ respectively with $\omega$. $M$ and $N$ are the intersection points of $AC$ and $BD$ respectively with $KL$. $P$ and $Q$ are intersection points of $DM$ and $CN$ respectively with $AB$. Prove that $AP=BQ$.  

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