Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).

In the following figure, $ABCD$ is a cyclic quadrilateral in which $AC$ and $BD$ are its diagonals. If $\angle DBC=55°$, $\angle BAC=45°$ and $\angle BCD=k°$, then find the value of $k$.

$ABCD$ is a cyclic quadrilateral in which $BA$ and $CD$ when produced meet in $E$ and $EA=ED$ Prove that:

$AD\Vert BC$

$ABCD$ is a cyclic quadrilateral in which $BA$ and $CD$ when produced meet in $E$ and $EA=ED$ Prove that:

$EB=EC$