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 = 600Calculate;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 Mathematics![]() Form 3 Mathematics![]() 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 ![]() Form 3 Mathematics![]() 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 ![]() Form 2 Mathematics![]() Form 2 Mathematics![]() Form 2 Mathematics![]() 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. ![]() |
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