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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In the figure below, OABC is a rhombus drawn in a circle, centre O, of radius 3 cm. Angle AOC = 120°22/3/2024  angle properties of a circle  FORM 3 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 16 In the figure below, OABC is a rhombus drawn in a circle, centre O, of radius 3 cm. Angle AOC = 120°
Determine the total area of the shaded regions to 2 decimal places. (4 marks) ANGLE PROPERTIES OF A CIRCLE  FORM 2 LEVEL  KCSE 1996  PAPER 2  SECTION BIn the figure below, AOC represents a diameter of the circle with center O. The length of AB is equal to BC, and the angle ACD measures 25 degrees. The line EBF is a tangent to the circle at point B. Additionally, point G is located on the minor arc CD.
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 8  KCSE 2022  ANGLE PROPERTIES OF A CIRCLE  PAPER 2  FORM 3 LEVEL In the figure below, O is the centre of the circle. Points A, B, C and D lie on the circumference of the circle. Line AB is parallel to the straight line EDO and line FAE is a tangent to the circle at A. FAB = a°, DOA = b°, DCB = 70°
Determine the values of a and b. (4 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 = 20^0In the figure below DA is a diameter of the circle ABCDE centre O. AB = BC and angle DAC = 36°29/4/2023 In the figure below DA is a diameter of the circle ABCDE centre O. AB = BC and angle DAC = 36°ANSWER
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 = 60^{0}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.
Form 3 MathematicsForm 3 MathematicsForm 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 = 130^{0} and angle MKN = 40^{0}
Find the values of the following angles, stating the reasons in each case:
a) ∠MLN
b) ∠OLN c) ∠LNP d) ∠MPN Form 3 MathematicsForm 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 Form 2 MathematicsForm 2 MathematicsForm 2 Mathematics 
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