Question 166
A triangle $ABC$ with $\overline{AB} + \overline{BC} = 3 \overline{AC}$ is given. Its incircle has the center $I$ and touches the sides $AB$ in $D$ and $BC$ in $E$. Furthermore, $K$ and $L$ are the mirror points of $D$ and $E$ with respect to $I$.
Prove that the quadrilateral $ACKL$ is a chord quadrilateral.
Prove that the quadrilateral $ACKL$ is a chord quadrilateral.