KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
 CHORDS AND TANGENTS  FORM 3 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 21 In the figure below, points L, M, N and P are on the circumference of a circle centre O. Line LON is a diameter of the circle. PL = PN and angle NLM = 20°.
Find, giving a season in each case, the size of each of the following angles. (a) ∠ MPN; (2 marks) (b) ∠ PLN; (2 marks) (c) ∠ LPM; (2 marks) (d) ∠ MNP; (2 marks) (e) ∠ PMO; (2 marks)
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ALT B  CIRCLES, CHORDS AND TANGENTS   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 12In the figure below, PRQS is a circle of radius 17cm. Line PQ is a diameter of the circle and is perpendicular to chord RS at T.
ALT B  Circles, Tangents and Chords   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 5The figure below shows a circle centre O and external point X.
QUESTION 4  KCSE 2023  CIRCLES, CHORDS AND TANGENTS  PAPER 2  FORM 3 LEVELIn this question, use a ruler and a pair of compasses. The following figure shows a circle, centre O. A tangent to the circle at P is drawn. Construct another tangent to the circle to intersect the drawn tangent at an angle of 60°. (3 marks)
The following figure shows a quadrilateral PQRS and a circle passing through the vertices R and S29/12/2023 QUESTION 22  KCSE 2023  TRIGONOMETRY II  PAPER 1  FORM 3 LEVELThe following figure shows a quadrilateral PQRS and a circle passing through the vertices R and S. Lines PQ = PR = 2.7 cm, PS = 6 cm, SR = 7 cm and ∠PQR = 65°.
In the figure below, points A, B, C, and E lie on the circumference of the circle centre O28/12/2023 QUESTION 19  KCSE 2021  ANGLE PROPERTIES OF A CIRCLE  PAPER 2  FORM 3 LEVELIn the figure below, points A, B, C, and E lie on the circumference of the circle centre O. Line FAG is a tangent to the circle at A. Chord DE of the circle is produced to intersect with the tangent at F. Angle FAE = 30°, Angle EDC = 110° and Angle OCB =55°
QUESTION 5  KCSE 2021  Circles, Chords & Tangents  PAPER 2  FORM 3 LEVELThe figure below shows a circle and a point P outside the circle Using a ruler and pair of compasses, construct a tangent to the circle from P. (4 marks)
Two parallel chords AB = 4cm and CD = 10 cm lie on opposite sides of a centre O of a circle.19/12/2023 QUESTION 6  KCSE 2022  CIRCLES, CHORDS AND TANGENTS  PAPER 2  FORM 3 LEVEL Two parallel chords AB = 4cm and CD = 10 cm lie on opposite sides of a centre O of a circle. The perpendicular distance between the two chords is 7 cm.
Calculate the radius of the circle leaving the answer in surd form. (3 marks) In the figure below A, B, C and D are points on the circumference of the circle, centre O. A tangent to the circle at A intersects chord CD produced at E. Line AB is parallel to line EC. Angle AED = 45 degrees and angle ABD = 40 degrees.KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 23In 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 = 38^{0}. Calculate the size of angle CTB (3mks)In the figure below, points L, M,N and P are on the circumference of a circle centre O. LON is a diameter of the circle PL = PN and angle NLM = 20^0
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.
Form 3 MathematicsForm 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 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. 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).
Form 3 MathematicsForm 3 MathematicsForm 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. 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. Form 3 MathematicsForm 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)

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