J P Mohindru and Bharat Mohindru Solutions for Chapter: Circles, Exercise 4: COMPETITION FILE

In the given figure, $\mathrm{AB}$ is a chord of the circle and $\mathrm{AOC}$ is its diameter such that $\angle \mathrm{ACB}=50°$. If $\mathrm{AT}$ is the tangent to the circle at a point $\mathrm{A},$ then $\angle \mathrm{BAT}$ is equal to

From a point $\mathrm{P}$ which is at a distance of $13 \mathrm{cm}$ from the centre $\mathrm{O}$ of a circle of radius $5 \mathrm{cm}$, the pair of tangents $\mathrm{PQ}$ and $\mathrm{PR}$ to the circle are drawn. Then the area of the quadrilateral $\mathrm{PQOR}$ is

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.

If two tangents inclined at an angle $60°$ are drawn to a circle of radius $3 \mathrm{cm}$, then length of each tangent 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