In the given figure, quad. $\mathrm{ABCD}$ is circumscribed, touching the circle at $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$. If $\mathrm{AP}=5 \mathrm{cm}, \mathrm{BC}= 7 \mathrm{cm}$ and $\mathrm{CS}=3 \mathrm{cm}$. Then, the length $\mathrm{AB}=$?.

In the given figure, quad. $ABCD$ is circumscribed, touching the circle at $P, Q, R$ and $S$. If $AP=6 \mathrm{cm}, BP=5 \mathrm{cm}$, and $DR=4 \mathrm{cm}$ then perimeter of quad. $ABCD$ is

In the given figure, $O$ is the centre, $AB$ is a chord and $AT$ is the tangent at $A$. If $\angle AOB=100°$, then find $\angle BAT$.

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