In the given figure, a circle is inscribed in a quadrilateral $ABCD$ touching its sides $AB, BC, CD$ and $AD$ at $P, Q, R$ and $S$, respectively. If the radius of the circle is $10 \mathrm{cm}$, $BC=38 \mathrm{cm}, PB=27 \mathrm{cm}$ and $AD\perp CD$ then the length of $CD$ is

 

In the given figure, $∆\mathrm{ABC}$ is right-angled at $\mathrm{B}$ such that $\mathrm{BC}=6 \mathrm{cm}$ and $\mathrm{AB}=8 \mathrm{cm}$. A circle with centre $\mathrm{O}$ has been inscribed inside the triangle. $\mathrm{OP}\perp \mathrm{AB}, \mathrm{OQ}\perp \mathrm{BC}$ and $\mathrm{OR}\perp \mathrm{AC}$. If $\mathrm{OP}=\mathrm{OQ}=\mathrm{OR} =x \mathrm{cm}$ then $x=$?

Quadrilateral $ABCD$ is circumscribed to a circle. If $AB=6 \mathrm{cm}, BC=7 \mathrm{cm}$, and $CD=4 \mathrm{cm}$ then the length of $AD$ is

In the given figure, $PA$ and $PB$ are tangents to the given circle such that $PA=5 \mathrm{cm}$ and $\angle APB=60°$. The length of chord $AB$ is

In the given figure, $DE$ and $DF$ are tangents from an external point $D$ to a circle with centre $A$. If $DE=5 \mathrm{cm}$ and $DE\perp DF$ then the radius of the circle is

In the given figure, three circles with centres $A, B, C$ are respectively touch each other externally. If $AB=5 \mathrm{cm}, BC=7 \mathrm{cm}$ and $CA=6 \mathrm{cm}$ then the radius of the circle with centre $A$ is

In the given figure, $AP, AQ$ and $BC$ are tangents to the circle. If $AB=5 \mathrm{cm}, AC=6 \mathrm{cm}$ and $BC=4 \mathrm{cm}$ then the length of $AP$ is

In the given figure, $O$ is the centre of two concentric circles of radii $5 \mathrm{cm}$ and $3 \mathrm{cm}$. From an external point $P$ tangents $PA$ and $PB$ are drawn to these circles. If $PA=12 \mathrm{cm}$ then $PB$ is equal to