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Quiz Chapter 5: Circles

10 questions · Form 2 Mathematics Bab 5: Circles

Question 1 of 10Score: 0

What is the longest chord in a circle?

Full Question List & Answer Key

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?

  1. Radius
  2. Arc
  3. Diameter
  4. Tangent
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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.

  1. 10 cm
  2. 14 cm
  3. 20 cm
  4. 6 cm
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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)

  1. 7 cm
  2. 14 cm
  3. 3.5 cm
  4. 49 cm
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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.

  1. 85°
  2. 95°
  3. 185°
  4. 275°
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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)

  1. 154 cm²
  2. 616 cm²
  3. 44 cm²
  4. 308 cm²
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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?

  1. 70°
  2. 110°
  3. 180°
  4. 220°
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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)

  1. 22 cm
  2. 36 cm
  3. 44 cm
  4. 58 cm
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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)

  1. 45°
  2. 90°
  3. 60°
  4. 120°
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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)

  1. 22 cm
  2. 11 cm
  3. 44 cm
  4. 33 cm
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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)

  1. 21 cm
  2. 14 cm
  3. 42 cm
  4. 28 cm
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Answer: A

(120360) × 2 × (227) × r = 44 => (13) × (447) × r = 44 => r = 44 × 3 × (744) = 21 cm.

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