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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 In the figure below, EAF and EDG are tangents to the circle. AB is parallel to DC, angle FAB = 46° and angle AED = 110°.
Find the values of angles P and q. (3mks)Worked Answer:
A chord PQ of length 15cm subtends an angle of 65º at the circumference centre O. Find the radius of the circle. (3mks)Worked Solution
In the figure below AB and AC are tangents to the circle center O at B and C respectively, the angle AOC = 600
Calculate;a) The length of AC (2mks)b) The area of triangle OAC (2mks)c) The area of minor sector COD (2mks)d) The area of the shaded region (4mks)
Worked Solution:
a) Construct triangle ABC such that AB = 8cm, BC = 6cm and angle ABC = 300 (3mks)b) Measure the length of AC (1mk)c) Draw a circle that touches the vertices A, B and C (2mks)d) Measure the radius of the circle (1mk)c) Hence or otherwise, calculate the area of the circle outside triangle (3mks)
Worked Solution:
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, PQRS is a cyclic quadrilateral. PQ = QR, PQR =105° and PS is parallel to QR.
Determine the size of.
(a) ∠ PSR (b)∠ PQS.
answer
Form 3 Mathematics
In the figure below, K M and N are points on the circumference of a circle centre O.
The points K, O, M and p are on a straight line. PN is a tangent to the circle at N.Angle KOL = 1300 and angle MKN = 400 
Find the values of the following angles, stating the reasons in each case:
a) ∠MLN
b) ∠OLN c) ∠LNP d) ∠MPN
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 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 2 Mathematics
In the figure below is O the center of the circle ABCD and AOD in a straight line
If AB = BC and angle DAC = 400, Calculate angle BAC.
Answer
Form 2 Mathematics
In the figure below, ABCD is a cyclic quadrilateral. Point O is the centre of the circle. Angle ABO = 30° and angle ADO - 40°.
Calculate the size of angle BCD.
answer
Form 2 Mathematics
In the figure below DA is a diameter of the circle ABCD centre O, radius 10cm. TCS is a tangent to the circle at C, AB=BC and angle DAC= 380
a) Find the size of the angle;
(i) ACS; (ii) BCA b) Calculate the length of: (i) AC (ii) AB
answers
Form 2 Mathematics
An angle of 1.8 radians at the centre of a circle subtends an area of length 23.4cm
Find; a) The radius of the circle b) The area of the sector enclosed by the arc and the radii.
answer
Form 2 Mathematics
In the figure below R, T and S are points on a circle centre O PQ is a tangent to the circle at T. POR is a straight line and angle QPR = 200
Find the size of angle RST
answer
Form 3 MathematicsIn the figure below, points O and P are centers of intersecting circles ABD and BCD respectively. Line ABE is a tangent to circle BCD at B. Angle BCD = 420 
Answer
Form 2 Mathematics | Topical Questions and AnswersOn The figure below lines ABC and DC are tangents to the circle at B and D respectively ∠ACD = 400 and ∠ABE = 600 
Giving reasons find the size of:
ANSWER
Free 1999 K.C.S.E Mathematics Topical Question & Answers Paper 1The figure below shows two circle ABPQ and ABSR intersecting at A and B. PBS, QART and ABU are straight lines. The line UST is a tangent to a circle ABSR at S. ∠BPQ = 800, ∠PBU = 1150 and ∠BUS = 700 
Find the values of the following angles, stating your reason in each case.
ANSWER
Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2
The figure below represents a rectangle PQRS inscribed in a circle centre 0 and radius 17cm . PQ = 16 cm.
​Calculate
answer
Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2
In the figure below, QOT is a diameter. ∠QTR = 480, ∠TQR = 760 and ∠SRT = 370
Calculate
ANSWER
In the figure below PQR is the tangent to circle at Q. TS is a diameter and TSR and QUV are straight lines. QS is parallel to TV. Angles SQR = 400 and angle TQV = 550
Find the following angles, giving reasons for each answer
In the figure below AOC is a diameter of the circle centre O; AB = BC and ∠ACD = 250, EBF is a tangent to the circle at B. G is a point on the minor arc CD.
MARKING SCHEME
In the figure below CP= CQ and ∠CQP = 1600. If ABCD is a cyclic quadrilateral, find ∠BAD.
2 marks
marking scheme
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