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November 1st, 2019, 08:24 AM   #1
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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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