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Quiz Chapter 6: Angles and Tangents of Circles

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

Question 1 of 10Score: 0

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

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 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°.

2. 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°.

3. If arc AB and arc CD of a circle have equal lengths, which statement is true regarding their subtended angles at the circumference?

  1. The angle subtended by arc AB is larger
  2. The angle subtended by arc CD is larger
  3. The angles subtended by both arcs are equal
  4. The sum of both angles is 180°
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Answer: C

Arcs of equal length in the same circle subtend equal angles at the circumference.

4. 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°).

5. 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.

6. A cyclic quadrilateral has interior angles x, 2x, y, and 3y in order around the circle. What is the value of x?

  1. 30°
  2. 45°
  3. 60°
  4. 90°
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Answer: C

Opposite angles sum to 180°. So x + y = 180° and 2x + 3y = 180°. Solving x = 180° - y: 2(180° - y) + 3y = 180° => 360° + y = 180° (using adjacent cyclic pairing): x + 2x = 180° => 3x = 180° => x = 60°.

7. 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.

8. If the angle subtended at the centre of a circle by arc AB is 110°, what is the angle subtended at the circumference by the same arc AB?

  1. 220°
  2. 55°
  3. 110°
  4. 70°
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Answer: B

Angle at circumference = Angle at centre2 = 110° / 2 = 55°.

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. 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°.

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