At one end $\mathrm{A}$ of a diameter $\mathrm{AB}$ of a circle of radius $5 \mathrm{cm},$ tangent $\mathrm{XAY}$ is drawn to the circle. The length of the chord $\mathrm{CD}$ parallel to $\mathrm{XY}$ and at a distance $8 \mathrm{cm}$ from $\mathrm{A}$ is

In figure, $\mathrm{AT}$ is tangent to the circle with centre $\mathrm{O}$ such that $\mathrm{OT}=4 \mathrm{cm}$ and $\angle \mathrm{OTA}=30°$. Then $\mathrm{AT}$ is equal to

In figure, if $\mathrm{O}$ is the centre of the circle, $\mathrm{PQ}$ is a chord and the tangent $\mathrm{PR}$ at $\mathrm{P}$ makes an angle of $50°$ with $\mathrm{PQ}$, then $\angle \mathrm{POQ}$ is equal to

In fig., if $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle with centre $\mathrm{O}$ such that $\angle \mathrm{APB}=50°$, then angle $\angle \mathrm{OAB}$ is equal to.

In figure, if $\mathrm{PQR}$ is the tangent to a circle at $\mathrm{Q}$ whose centre is $\mathrm{O}, \mathrm{AB}$ is a chord parallel to $\mathrm{PR}$ and $\angle \mathrm{BQR}=70°$, then $\angle \mathrm{AQB}$ is equal to

In the figure, $\mathrm{ABC}$ is an isosceles triangle in which $\mathrm{AB}=\mathrm{AC}$ and $\angle \mathrm{ABC}=50°$. Then $\angle \mathrm{BDC}$ is equal to:

In the figure, $\mathrm{O}$ is the centre of the circle with $\mathrm{AC}$ as diameter. If $\angle \mathrm{ADB}=120°$ and the length of the radius of the circle is $6 \mathrm{cm}$, then the area of the triangle $\mathrm{ABC}$ is

In the figure, $\mathrm{ABC}$ is a right-angled triangle, right-angled at $\mathrm{A}$. If $\mathrm{AB}=3 \mathrm{cm}, \mathrm{BC}=5 \mathrm{cm}$ and $\mathrm{AC}=4 \mathrm{cm}$ then the radius of the circle is: