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ANGLE PROPERTIES OF A CIRCLE | CIRCLES: CHORDS AND TANGENTS | | PROPERTIES OF CHORDS INTERSECTING EXTERNALLY | FORM 3 | PAPER 2 QUESTIONS | SECTION A
Chords AB and CD of a circle meet at X.
If AB = 8cm, BX = 5cm and DX = 6. Calculate the length of chord CD. (3mks)
WORKED ANSWER:
Let CD be x
CX * DX = AX * BX (PROPERTIES OF CHORDS INTERSECTING EXTERNALLY)
(X + 6)6 = 13 * 5 6X + 36 = 65 6X = 29 X = 29/6 = 4.83CM Form 2 Mathematics
An arc of a circle subtends an angle of 150° at the circumference of the circle. Calculate the angle subtended by the same arc at the centre of the circle.
ANSWER
Form 3 Mathematics
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.
answer
Form 3 Mathematics
In the figure below, P, Q, R and S are points on the circle with centre O. PRT and USTV are straight lines. Line USTV is a tangent to the circle at S. Z.
RST = 50° and Z. RTV = 150°. 
a) Calculate the size of
i)<QRS ii)<USP iii)<PQR b) Given that RT = 7 cm and ST = 9 cm, calculate to 3 significant figures i)Length of line PR ii)The radius of the circle
answers
Form 3 Mathematics
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.
answer
Form 2 Mathematics
A minor arc of a circle subtends an angle of 105 at the centre of the circle. If the radius of the circle is 8.4 cm, find the length of the major arc (Take π= 22/7).
answer
Form 3 Mathematics
The figure below shows a circle, centre, 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
Answer
Form 3 Mathematics
In the figure below, O is the centre of the circle. A, B, C and D are points on the circumference of the circle. Line AB is parallel to line DC and angle ADC = 55°.
Determine the size of angle ACB
answer
Form 3 Mathematics
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.
answer
Form 3 Mathematics
In the figure below OS is the radius of the circle centre O. Chords SQ and TU are extended to meet at P and OR is perpendicular to QS at R. OS = 61cm, PU=50cm, UT=40cm and PQ =30cm.
a) Calculate the lengths of:
i) QS: ii) OR c) Calculate, correct to 1 decimal place: i)The size of angle ROS: ii) The length of the minor arc QS.
answers
Form 3 Mathematics
In the figure below, BOD is the diameter of the circle centre O. Angle ABD = 300 and angle AXD = 700.
Determine the size of :
a) Reflex angle BOC b) angle ACO.
answer
Form 3 Mathematics
A minor arc of a circle subtends an angle of 105 at the centre of the circle. If the radius of the circle is 8.4cm, find the length of the major arc ( take ? = 22/7)
answer
Form 2 Mathematics
The area of a sector of a circle, radius 2.1cm, is 2.31cm^2. The arc of the sector subtends an angle θ, at the centre of the circle. Find the value of θ in radians to
2 correct decimal places
answer
Form 3 Mathematics
In the figure below, PR is a diameter of the circle center O. Points P, Q, R and S are on the circumference of the circle. Angle PRQ = 72, QS = QP and line USV
is tangent to the circle at S. 
Giving reasons, Calculate the size of
(a) ˂ QPR (b) ˂ PQS (c) ˂ OQS (d) ˂ RTS (e) ˂ RSV
answers
Form 3 Mathematics
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 
(a) Calculate the length of chord VU.
(b) If WX =3 cm and VX: XU= 2:3, find SX.
answer
Form 3 Mathematics
The diagram below shows a circle ABCDE. The line FEG is a tangent to the circle at point E. Line DE is parallel to CG,
Answer
Form 3 Mathematics
In the figure below, P, Q, R and S are points on the circle centre O. PRT and USTV are straight lines.
Line USTV is a tangent to the circle at S, ZRST = 50° and LRTV = 150°. 
(a) Calculate the size of:
(i) angle ORS; (ii) angle USP; (iii) angle PQR. (b) Given that RT = 7 cm and ST 9 cm, calculate to 3 significant figures: (i) the length of line PR; (ii) the radius of the circle.
answers
Form 3 Mathematics
In the figure below, O is the centre of the circle which passes through the points T, C and D. Line TC is parallel to OD and line ATB is a tangent to the circle at T. Angle DOC = 36°.
Calculate the size of angle CTB.
answer
Form 3 Mathematics
The figure below shows two sectors in which CD and EF are arcs of concentric circles, centre O. Angle COD = 2/3 radians and CE = DF = 5 cm.
If the perimeter of the shape CDFE is 24 cm, calculate the length of OC.
answer
Form 3 Mathematics
In the figure below, AT is a tangent to the circle at A TB = 480, BC = 5 cm and CT = 4 cm.
Calculate the length AT.
answer
Form 3 Mathematics
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. (2mks)
Answer
Form 3 Mathematics
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
answer
Form 3 Mathematics
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
answer
Form 3 Mathematics
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
Answer
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