In the following diagram, there are two circles externally tangent to each other and there is a common tangent $\mathrm{CP}$ touch the circles at $\mathrm{C}$ and $\mathrm{D}·\mathrm{AC}$ and $\mathrm{BD}$ are the radii of the two circles. If $\mathrm{AC}=15$ and $\mathrm{BD}=6$, find the distance between $\mathrm{C}$ and $\mathrm{D}.$

An equilateral triangle $\mathrm{ABC}$ is tangent to a circle, with centre $\mathrm{O}$, at the midpoint $\mathrm{D} .$ If $\mathrm{C}$ lies on the circumference of the circle and its radius is $6 \mathrm{cm}$, find the area of the overlapping region.

In the following figure one side of a square is tangent to the circle, as shown here. If each side of the square be $24 \mathrm{cm}$, what would be the radius of the circle?

In a right angled triangle $\angle \mathrm{B}$ and $\angle \mathrm{A}$ are acute angles. If $\angle \mathrm{A}-\angle \mathrm{B}=\mathrm{k}$, where $\mathrm{A}$ and $\mathrm{B}$ are integers, then how many integer values can $\mathrm{k}$ take?

$\mathrm{ABCD}$ is a quadrilateral in which $\frac{\mathrm{z}}{\mathrm{y}}=\frac{\mathrm{y}}{\mathrm{x}}=\frac{\mathrm{x}}{\mathrm{w}}=\mathrm{r}$ and $\mathrm{k}$ is an integer. Also $\{\mathrm{w},\mathrm{x}\}<90$ and $\{\mathrm{y},\mathrm{z}\}>90$ then the difference between the greatest angle and smallest angle (i.e., $\mathrm{z}-\mathrm{w}$ ) is