Problem

Source: 2023 Turkey Tst D1 P1

Tags: geometry, trapezoid, circumcircle



Let $ABCD$ be a trapezoid with $AB \parallel CD$. A point $T$ which is inside the trapezoid satisfies $ \angle ATD = \angle CTB$. Let line $AT$ intersects circumcircle of $ACD$ at $K$ and line $BT$ intersects circumcircle of $BCD$ at $L$.($K \neq A$ , $L \neq B$) Prove that $KL \parallel AB$.