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Quiz Chapter 6: Angles and Tangents of Circles

10 questions · Form 3 Mathematics Bab 6: Angles and Tangents of Circles

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Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. According to the Alternate Segment Theorem, the angle between a tangent and a chord through the point of contact is equal to:

  1. The angle in the alternate segment
  2. The angle at the centre
  3. The adjacent angle on the chord
  4. 90°
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Answer: A

The Alternate Segment Theorem states that the angle between a tangent and a chord equals the angle subtended by that chord in the alternate segment.

2. Point A is an external point 10 cm away from the centre O of a circle with radius 6 cm. Calculate the length of the tangent line drawn from A to the circle.

  1. 8 cm
  2. 4 cm
  3. 16 cm
  4. 12 cm
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Answer: A

Tangent length = √10² - 6² = √100 - 36 = √64 = 8 cm.

3. In a circle, chords AB and CD intersect. If PQ represents a tangent at P and chord PR makes an angle of 52° with tangent PQ, what is the angle subtended by chord PR in the alternate segment?

  1. 52°
  2. 38°
  3. 104°
  4. 128°
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Answer: A

By the Alternate Segment Theorem, the angle in the alternate segment equals the angle between the tangent and chord, which is 52°.

4. How many tangents can be drawn to a circle from a single point located outside the circle?

  1. 1
  2. 2
  3. 4
  4. Infinitely many
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Answer: B

Exactly two tangents can be drawn to a circle from any given external point.

5. An angle subtended at the circumference by a diameter (in a semicircle) is always equal to:

  1. 45°
  2. 60°
  3. 90°
  4. 180°
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Answer: C

An angle in a semicircle subtended by the diameter is always a right angle (90°).

6. What is the sum of opposite interior angles in a cyclic quadrilateral?

  1. 90°
  2. 180°
  3. 270°
  4. 360°
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Answer: B

Opposite interior angles in a cyclic quadrilateral are supplementary, meaning their sum is 180°.

7. The exterior angle of a cyclic quadrilateral is always equal to:

  1. The adjacent interior angle
  2. The interior opposite angle
  3. Half of the interior opposite angle
  4. 90°
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Answer: B

The exterior angle formed by extending one side of a cyclic quadrilateral is equal to the interior opposite angle.

8. What is the relationship between the angle at the centre and the angle at the circumference subtended by the same arc?

  1. Angle at centre is equal to angle at circumference
  2. Angle at centre is half the angle at circumference
  3. Angle at centre is twice the angle at circumference
  4. The sum of both angles is always 180°
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Answer: C

By circle theorems, the angle subtended by an arc at the centre is twice the angle subtended by the same arc at any point on the circumference.

9. If arc AB subtends an angle of 40° at the circumference, what is the angle subtended by arc AB at the centre?

  1. 20°
  2. 40°
  3. 80°
  4. 140°
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Answer: C

Angle at centre = 2 × Angle at circumference = 2 × 40° = 80°.

10. Two tangents from an external point T touch a circle at P and Q. If angle PTQ = 40°, what is angle POQ at the centre of the circle?

  1. 140°
  2. 80°
  3. 100°
  4. 120°
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Answer: A

Quadrilateral OPTQ has right angles at P and Q (90° each). Thus, angle POQ + angle PTQ = 180° => POQ = 180° - 40° = 140°.

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