# 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 120o 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 172o 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 240o. 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 55o 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 60o 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 200o 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 120o 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 ao 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 $\angle PQR$ 