Question 32 of 50beginner💡 UnderstandShort Answer2 marks

The diameter of a circle is AB. Point C is on the circumference. What is the measure of the ∠\angleACB? Explain your reasoning.

Correct Answer

90°

Exercise: END-OF-CHAPTER EXERCISES | Q: 6 | (Page 23)
For More Understanding

Explanation

According to Theorem 9 from the provided context, the angle subtended by an arc at the centre of the circle is double the angle subtended by the arc at any point on the circle outside the arc. Since AB is the diameter, the arc AFB is a semicircle, which subtends a straight angle of 180° at the centre. Point C is on the circumference outside the arc AFB, so the angle ∠ACB is half the angle subtended at the centre. Thus, ∠ACB = 180° / 2 = 90°.

Solution Steps

  1. Step 1: Since AB is the diameter, the arc AFB is a semicircle, which subtends an angle of 180° at the centre of the circle.

  2. Step 2: According to Theorem 9, the angle subtended by an arc at the centre is double the angle subtended by the arc at any point on the circle outside the arc.

  3. Step 3: Point C is on the circumference outside the arc AFB, so ∠ACB = 1/2×1802 \times 180° = 90°.

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