In the diagram, O is the centre of the circle and PQRS is a cyclic quadrilateral. Find the value of x   

In the diagram \[\left| PR \right|=\left| QR \right|\] and $\left| PR \right|=\left| RS \right|=\left| SP \right|$ , calculate the size of $\angle QRS$

POR is a sector of a circle centre O, radius 4cm, if $\angle PQR={{30}^{{}^\circ }}$. Find, correct to 3 significant figures, the area of sector POR $\pi =\tfrac{22}{7}$ 

In the diagram, angle 200^o is subtended at the centre of the circle. Find the value of x

An arc of a circle subtends an angle of 60^o at the centre. If the radius of the circle 3cm, find in terms of π, the length of the arc

In the diagram, $\left| TP \right|=12cm$ and it is  6cm from O, the centre of the circle Calculate $\angle TOP$

In the diagram $\overline{MN}$is a chord of a circle KMN centre O and radius 10cm. If $\angle MON={{140}^{\circ }}$, find, correct to the nearest cm, the length of the chord MN

In the diagram, O  is the centre of the circle $\angle QPS={{100}^{\circ }},\text{ }\angle PSQ={{60}^{\circ }}\text{ and }\angle QSR={{80}^{\circ }}$ Calculate $\angle SQR$

In the diagram, TS is a tangent to the circle at S . $\left| PR \right|=\left| RS \right|$ and $\angle PQR={{117}^{\circ }}$. Calculate $\angle PST$

In the diagram, TS is a tangent to the circle at S . $\left| PR \right|=\left| RS \right|$ and $\angle PQR={{117}^{\circ }}$. Calculate $\angle PST$