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# Form 3 Mathematics: Circles, Chords and Tangents Questions and Answers

Form 3 Mathematics: Circles, Chords and Tangents Questions and Answers

Lessons (**23**) * SHARE*

- 1.
The figure below represents the cross-section of a metal bar. The cross section is in the form of a major segment of the circle. M is the midpoint
of AB and CM is perpendicular to AB. Given that AB=CM=8cm.
Calculate the area of the cross section.

8m 53s - 2.
A chord AB of length 13 cm subtends an angle of #67^0# at the circumference of a circle center O. Find the radius of the circle.

4m 2s - 3.
In the figure below, O is the centre of the circle of radius 2.8cm. Angle AOB=#150^0#.
Determine the area of the shaded segment.

3m 30s - 4.
In the figure below O is the centre of a circle whose radius is 8cm. BA and BC are tangents to the circle. PD is a diameter of the circle
and AC is a chord of length 8cm. Angle ABC=#120^0#. ARC is an arc of a circle centre B and radius 4.6cm.
Calculate the area of the shaded region.

10m 44s - 5.
The figure below shows two pulleys with centers A and B and of radii 10cm and 5cm respectively. S and R are contact points of the belt
with the pulleys. The distance between the centers of the two pulleys is 50cm, and #angle#SAB=#84.26^0#. A belt is tied around the two pulleys
as shown. Calculate the total length of the belt.

7m 8s - 6.
In the figure below AB is a tangent to the circle centre O and radius 12cm. the area of the triangle AOB is 120#cm^2#. OXB is a straight line.
Calculate XB.

3m 40s - 7.
The figure below (not drawn to scale) shows a triangle ABC inscribed in a circle. AB =6cm, BC=9cm and AC=10cm.
Calculate:
(a) The radius of the circle
(b) The area of the shaded parts.

8m 7s - 8.
In the figure below O is the center of a circle whose radius is 5cm. AB=8cm and #angle#AOB is obtuse angle.
Calculate the area of the major segment.

4m 21s - 9.
The figure below represents a circle a diameter 28 cm with a sector subtending an angle of #75^0# at the center.
Find the area of the shaded segment to 4 significant figures

2m 23s - 10.
The figure below represents a rectangle PQRS inscribed in a circle centre 0 and radius 17cm . PQ = 16cm.
Calculate
(a) The length PS of the rectangle
(b) The angle POS
(c) The area of the shaded region

5m 57s - 11.
In the figure below, BT is a tangent to the circle at B. AXCT and BXD are straight lines AX = 6cm, CT = 8cm, BX = 4.8 cm and XD = 5cm.
Find the length of
(a) XC
(b) BT

3m 42s - 12.
Chords XY and PQ of a circle intersect at a point M inside the circle. Given that MX = 8cm, XY = 14cm and MP = 4cm, calculate the length of MQ.

2m 33s - 13.
The figure below shows two circles each of radius 7cm, with centers at X and Y. The circles touch each other at point Q.
Give that AXD = BYC =# 120^0# and lines AB, XQY and DC are parallel,
calculate the area of:
a) Minor sector XAQD (Take ? #22/7#)
b) The shaded regions.

11m 36s - 14.
The figure below shows a circle, center, O of radius 7cm. TP and TQ are tangents to the circle at points P and Q respectively.
OT =25cm.
Calculate the length of the chord PQ

7m 18s - 15.
In the figure below, PQR is an equilateral triangle of side 6 cm. Arcs QR, PR and PQ arcs of circles with centers at P, Q and R respectively.
Calculate the area of the shaded region to 4 significant figures

5m 14s - 16.
In the figure below AB is a diameter of the circle. Chord PQ intersects AB at N. A tangent to the circle at B meets PQ produced at R. Given that PN = 14cm, NB = 4 cm and BR = 7.5 cm, calculate the length of:
(a) NR
(b) AN

6m 17s - 17.
In the figure below, AT is a tangent to the circle at A TB = #48^0#, BC = 5 cm and CT = 4 cm.
Calculate the length AT.

1m 31s - 18.
(a) In the figure below, lines NA and NB represent tangents to a circle at points A and B. Use a pair of compasses and ruler only to construct the circle.
(b) Measure the radius of the circle.

8m 12s - 19.
In the figure below, the tangent ST meets chord VU produced at T. Chord SW passes through the centre, O, of the circle and intersects
chord VU at X. Line ST = 12 cm and UT =8cm
(a) Calculate the length of chord VU.
(b) If WX =3 cm and VX:XU= 2:3, find SX.

4m 35s - 20.
In the figure below OS is the radius of the circle centre O. Chord SQ and TU are extended to meet P and OR is perpendicular to QS at R. OS=61cm, PU=50cm, UT=40cm and PQ=30cm.
(a) Calculate the length of:
(i) QS
(ii) OR
(b) Calculate, correct to 1 decimal place:
(i) The size of angle ROS
(ii) The length of the minor arc QS.

11m 36s - 21.
An arc 11 cm long, subtends an angle of 70° at the centre of a circle.
Calculate the length, correct to one decimal place, of a chord that subtends an angle of 90° at the centre of the same circle.

4m 44s - 22.
Using a ruler and a pair of compasses only, construct:
(a) A triangle LMN in which LM = 5 cm, LN = 5.6 cm and MLN = #45^0# .
(b) The circle that touches all the sides of the triangle

8m 21s - 23.
In the figure below, AB is a tangent to the circle, centre O and radius 6 cm.
The arc AC subtends an angle of 60° at the centre of the circle.
Calculate the area of the shaded region, correct to 1 decimal place.

4m 36s