10 questions · Form 2 Mathematics Bab 5: Circles
What is the longest chord in a circle?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. What is the longest chord in a circle?
Answer: C
The diameter passes through the centre of the circle and connects two points on the circumference, making it the longest chord.
2. 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.
3. If the area of a circle is 154 cm², find its radius. (Take π = 227)
Answer: A
πr² = 154 => (227)r² = 154 => r² = 154 × (722) = 49 => r = 7 cm.
4. 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°.
5. Find the area of a circle with a diameter of 14 cm. (Take π = 227)
Answer: A
Radius r = 142 = 7 cm. Area = πr² = (227) × 7² = 154 cm².
6. 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°.
7. Find the perimeter of a semicircle with a radius of 7 cm. (Take π = 227)
Answer: B
Perimeter = Arc length of semicircle + Diameter = (πr) + 2r = ((227) × 7) + 2(7) = 22 + 14 = 36 cm.
8. A sector has an area of 38.5 cm² and a radius of 7 cm. Calculate the central angle θ. (Take π = 227)
Answer: B
(θ / 360) × (227) × 7² = 38.5 => (θ / 360) × 154 = 38.5 => θ / 360 = 0.25 => θ = 90°.
9. 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.
10. 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.