Waecmaths
Title  waecmaths question 

Question 17 
A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord. 
Question 19 
In the diagram $\overline{VX}$is a tangent to the tangent to the circle UYW at W. If $WY\parallel UV$, $\angle UYW={{95}^{\circ }}$ and $\angle UWY={{46}^{\circ }}$find $\angle UVW$ 
Question 23 
In the diagram, O is the centre of the circle, $OM\parallel XZ$and $\angle ZOM={{25}^{\circ }}$. Calculate $\angle XYZ$ 
Question 24 
A chord 7cm long, is drawn in a circle with radius 3.7cm. Calculate the distance of the chord from the centre of the circle 
Question 32 
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 
Question 39 
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 $\pi =\tfrac{22}{7}$] 
Question 41 
Determine the value of m in the diagram 
Question 44 
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 $\angle SQR$

Question 16 
The length of the minor and major arcs of a circle are 54cm and 126cm respectively. Calculate the angle of the major sector 
Question 17 
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 $\pi =\tfrac{22}{7}$] 
Question 20 
In the diagram O is the centre of the circle PQRS and $\angle PSR={{86}^{\circ }}$, if $\angle POR={{x}^{\circ }}$ find x 
Question 21 
The diagram is a circle centre O, If $\angle SPR=2m$ and $\angle SQR=n$ express m in terms of n 
Question 41 
The diagram is a circle with centre O. PRST are points on the circle. Find the value of $\angle PRS$ 
Question 42 
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 $\left PQ \right$ 
Question 44 
In the diagram, $\left SR \right=\left QR \right,\text{ }\angle SRP={{65}^{{}^\circ }},$$\text{and }\angle RPQ={{48}^{{}^\circ }}$ find $\angle PRQ$ 
Question 5 
In the diagram OP and OR are radii, \[\left PQ \right=\left QR \right\] and reflex $\angle POR$ is 240^{o}. Calculate the value of x

Question 19 
The perimeter of a sector of a circle 4cm is $(\pi +8)cm$ . Calculate the angle of the sector 
Question 24 
A circle is divided into two sectors in the ratio 3 : 7. If the radius of the circle is 7cm, Calculate the length of the minor arc of the arc 
Question 22 
In the diagram, the tangent MN makes an angle of 55^{o} with the chord PS. If O is the centre of the circle, find $\angle RPS$ 
Question 31 
In the diagram, O is the centre of the circle, $\angle SQR={{60}^{{}^\circ }},\angle SPR=y$ and $\angle SOR=3x$ find the value of (x + y) 
Question 35 
In the diagram GI is a tangent to the circle at H. If $EF\parallel GI$ calculate the size$\angle EHF$ 
Question 44 
In the diagram , O is the centre of the circle. Find the value of x 
Question 18 
In the diagram $\overline{YW}$is a tangent to the circle at X, $\left UV \right=\left VX \right$and $\angle VXW={{50}^{\circ }}$, find the value of $\angle UXY$ 
Question 20 
In the diagram, O is the centre of the circle \[\angle XOZ={{(10m)}^{\circ }}\] and \[\angle XWZ={{m}^{\circ }}\]calculate the value of m 
Question 22 
In the diagram, TS is a tangent to the circle at S . $\left PR \right=\left RS \right$ and $\angle PQR={{117}^{\circ }}$. Calculate $\angle PST$ 
Question 22 
In the diagram, TS is a tangent to the circle at S . $\left PR \right=\left RS \right$ and $\angle PQR={{117}^{\circ }}$. Calculate $\angle PST$ 
Question 41 
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 $\angle SQR$ 
Question 48 
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 
Question 19 
In the diagram, $\left TP \right=12cm$ and it is 6cm from O, the centre of the circle Calculate $\angle TOP$ 
Question 34 
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 
Question 38 
In the diagram, angle 200^{o} is subtended at the centre of the circle. Find the value of x 
Question 17 
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 $\pi =\tfrac{22}{7}$ 
Question 20 
In the diagram \[\left PR \right=\left QR \right\] and $\left PR \right=\left RS \right=\left SP \right$ , calculate the size of $\angle QRS$ 
Question 25 
In the diagram, O is the centre of the circle and PQRS is a cyclic quadrilateral. Find the value of x 
Question 35 
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$\pi=\tfrac{22}{7}$ 
Question 37 
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 $\pi =\tfrac{22}{7}$] 
Question 44 
In the diagram, PX is a tangent to the circle and PST is an equilateral triangle. Calculate $\angle PTS$ 
Question 46 
In the diagram. Find the size of the angle marked a^{o}^{} 
Question 15 
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 
Question 23 
In the diagram $\left SP \right=\left SR \right$ and $\angle PRS={{50}^{\circ }}$ Calculate $\angle PQR$ 