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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. 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°.

3. Points P, Q, and R lie on a circle with centre O. If reflex angle POR = 240°, what is the acute/obtuse angle PQR at the circumference?

  1. 120°
  2. 60°
  3. 240°
  4. 30°
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Answer: A

The subtended angle at circumference = Reflex angle at centre2 = 240° / 2 = 120°.

4. In a circle with centre O, PT is a tangent to the circle at point P. If OP = 5 cm and OT = 13 cm, calculate the length of tangent PT.

  1. 12 cm
  2. 8 cm
  3. 18 cm
  4. 10 cm
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Answer: A

Triangle OPT is right-angled at P. PT = √13² - 5² = √169 - 25 = √144 = 12 cm.

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 angle formed between a tangent line and the radius drawn to the point of contact?

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

A tangent to a circle is always perpendicular (90°) to the radius at the point of contact.

7. 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.

8. 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°.

9. In a cyclic quadrilateral ABCD, if angle A = 75°, what is the measure of its opposite angle C?

  1. 75°
  2. 105°
  3. 150°
  4. 285°
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Answer: B

Angle C = 180° - 75° = 105°.

10. If the angle between a tangent and a chord is 68°, what is the angle subtended by the major arc in the alternate segment?

  1. 68°
  2. 112°
  3. 136°
  4. 34°
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Answer: A

By the Alternate Segment Theorem, the angle in the alternate segment directly equals 68°.

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