$\mathrm{ABCD}$ is a cyclic quadrilateral $\mathrm{PQ}$ is a tangent at $\mathrm{B}$. If $\angle \mathrm{DBQ}=65°$. Find the value of $\angle \mathrm{BCD}$:

In the given figure, $\mathrm{AP}=3 \mathrm{cm},\mathrm{BA}=5 \mathrm{cm}$ and $\mathrm{CP}=2 \mathrm{cm}$. Find the value of $\mathrm{CD}$.

In the given figure, $O$ and $O\text{'}$ are the centers of the circle. Two circles of radii $13 \mathrm{cm}$ and $5 \mathrm{cm}$ touch internally each other. Find the distance between their centers.

A circle touches a quadrilateral $\mathrm{ABCD}$. Find the true statement

$\mathrm{O}$ and $\mathrm{O}\text{'}$ are the centers of two circles that touch each other externally at $\mathrm{P}$. $\mathrm{AB}$ is a common tangent. Find the value of $\angle APB$.

In the given figure, $\mathrm{AB}$ and $\mathrm{CD}$ are two common tangents to the two touching circle. If $\mathrm{CD}=6 \mathrm{cm}$, then $\mathrm{AB}$ is equal to :

$\mathrm{O}$ and $\mathrm{O}\text{'}$ are the centers of circle of radii $20 \mathrm{cm}$ and $37 \mathrm{cm}$. $\mathrm{AB}=24 \mathrm{cm}$. What is the distance $\mathrm{OO}\text{'}$?