DE-BUNDESWETTBEWERB 2020 Problem 3

Let $AB$ be the diameter of a circle $k$ and let $E$ be a point in the interior of $k$ . The line $AE$ intersects $k$ a second time in $C \ne A$ and the line $BE$ intersects $k$ a second time in $D \ne B$ .

Show that the value of $AC \cdot AE+BD\cdot BE$ is independent of the choice of $E$ .