10 questions · Form 2 Mathematics Bab 5: Circles
10 questions · plays in fullscreen
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. If the angle subtended by an arc at the circumference is 35°, what is the angle subtended by the same arc at the centre?
Answer: C
The angle at the centre is twice the angle at the circumference: 2 × 35° = 70°.
2. Calculate the circumference of a circle with a radius of 7 cm. (Take π = 227)
Answer: B
Circumference = 2πr = 2 × (227) × 7 = 44 cm.
3. In a cyclic quadrilateral ABCD, if ∠A = 85°, find the measure of the opposite angle ∠C.
Answer: B
Opposite angles of a cyclic quadrilateral sum up to 180°: ∠C = 180° - 85° = 95°.
4. How many lines of symmetry does a complete circle have?
Answer: D
A circle has infinitely many lines of symmetry because any line passing through its centre acts as a line of reflectional symmetry.
5. An arc subtends an angle of 60° at the centre of a circle of radius 21 cm. Find the length of the arc. (Take π = 227)
Answer: A
Arc length = (θ / 360°) × 2πr = (60360) × 2 × (227) × 21 = (16) × 132 = 22 cm.
6. Two angles, x and y, are subtended at the circumference by the same arc in a circle. If x = 48°, find y.
Answer: B
Angles subtended at the circumference by the same arc are equal. Therefore, y = x = 48°.
7. The angle at the centre of a sector is 120° and its arc length is 44 cm. Find the radius of the circle. (Take π = 227)
Answer: A
(120360) × 2 × (227) × r = 44 => (13) × (447) × r = 44 => r = 44 × 3 × (744) = 21 cm.
8. In a cyclic quadrilateral PQRS, if exterior angle at vertex R is 110°, what is the interior opposite angle ∠P?
Answer: B
An exterior angle of a cyclic quadrilateral is equal to its interior opposite angle. Thus, ∠P = 110°.
9. A chord of length 12 cm is at a distance of 8 cm from the centre of a circle. Calculate the radius of the circle.
Answer: A
The perpendicular bisector forms a right triangle with half the chord (6 cm) and distance (8 cm). Radius r = √6² + 8² = √36 + 64 = √100 = 10 cm.
10. In a circle with radius 13 cm, a chord is 5 cm away from the centre. What is the length of the chord?
Answer: B
Half chord = √13² - 5² = √169 - 25 = √144 = 12 cm. Full chord length = 2 × 12 = 24 cm.