In the diagram, O is the centre of the circle If PQ $PQ\parallel RS$and $\angle ONS={{140}^{\circ }}$find the size of $\angle POM$

In the diagram P, Q, R, S are points on the circle $R\overset{\wedge }{\mathop{Q}}\,S$ = 30^o, $P\overset{\wedge }{\mathop{R}}\,S$ = 50^o and $P\overset{\wedge }{\mathop{S}}\,Q$ = 20^o. What is the value of x^o + y^o ?

In the diagram PR is a diameter of the circle centre O. RS is a tangent at R and $\angle QPR={{58}^{\circ }}$, find $\angle QRS$

In the diagram, O is the centre of the circle and $\angle PQR={{106}^{\circ }}$ .Find the value of y

In the diagram $\left| SP \right|=\left| SR \right|$ and $\angle PRS={{50}^{\circ }}$ Calculate $\angle PQR$

A chord of length 6cm is drawn in a circle of radius 5cm. Find the distance of the chord from the centre of the circle

In the diagram. Find the size of the angle marked a^o

In the diagram, PX is a tangent to the circle and PST is an equilateral triangle. Calculate $\angle PTS$

XY is a chord of circle centre O and radius 7. The chord XY which is 8cm long subtends an angle of 120^o at the centre of the circle . Calculate perimeter of the minor segment[Take $\pi =\tfrac{22}{7}$]

An arc of a circle, radius 14cm is 18.33cm long Calculate correct to the nearest degree, the angle which the arc subtends at the centre of the circle Take$\pi=\tfrac{22}{7}$