Prove that the parallelogram circumscribing a circle is a rhombus.

In the adjoining figure, $PA$ and $PB$ are two tangents to the circle with centre $O$, such that $\angle AOB=110°$, then $\angle APB$ is

In the figure, $a, b, c$ are the sides of a right triangle where $c$ is the hypotenuse. Prove that the radius $r$ of the circle which touches the sides of the triangle is given by $r=\frac{a+b+c}{2}$.

In the adjoining figure, $PQ, RS$ and $XY$ are tangent at $A, B$ and $Z$ respectively. $AOB$ is the diameter of the circle. If $\angle AXO=25°$, find $\angle BOX$.