The diagram is a circle of radius $\left| OQ \right|=4cm$ . $\overline{TR}$ is a tangent to the circle at R. If  $\angle TPO={{120}^{{}^\circ }}$ find $\left| PQ \right|$ 

The diagram is a circle with centre O. PRST are points on the circle. Find the value of $\angle PRS$

The diagram is a circle centre O, If $\angle SPR=2m$ and $\angle SQR=n$ express m in terms of n

In the diagram O is the centre of the circle PQRS and $\angle PSR={{86}^{\circ }}$, if $\angle POR={{x}^{\circ }}$ find x

A sector of a circle which subtends 172^o at the centre of the circle has a perimeter of 600cm. Find, correct to the nearest cm, the radius of the circle [Take $\pi =\tfrac{22}{7}$]

The length of the minor and major arcs of a circle are 54cm and 126cm respectively. Calculate the angle of the major sector

In the diagram,  O is the centre of the circle $\overline{PR}$is a tangent to the circle at Q and $\angle SOQ={{86}^{\circ }}$ Calculate the value of $\angle SQR$

Determine the value of m in the diagram

A chord subtends an angle of 120^o at the centre of a circle of radius 3.5cm. Find the perimeter of the minor sector containing the chord[Take $\pi =\tfrac{22}{7}$]

In the figure, PQ is a tangent to the circle at R and UT is parallel to PQ if $\angle TRQ={{x}^{\circ }}$. Find $\angle URT$in terms of x