In figure 3.56, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following. (1) ∠AOB (2) ∠ACB (3) arc AB (4) arc ACB.

In figure 3.56, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.

(1) \(\angle AOB\) (2) \(\angle ACB\) (3) arc AB (4) arc ACB.

Figure: C is a point on the major arc AB; \(\angle ACB\) is inscribed in arc ACB.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: (1) \(60^\circ\) (2) \(30^\circ\) (3) \(60^\circ\) (4) \(300^\circ\)

(1) OA = OB = AB (radii and given), so \(\triangle AOB\) is equilateral and \(\angle AOB = 60^\circ\).

(2) By the inscribed angle theorem,

\[\angle ACB = \frac{1}{2}\angle AOB = 30^\circ\]

(3) m(arc AB) = measure of its central angle = \(60^\circ\).

(4) Arc ACB is the major arc:

\[m(\text{arc ACB}) = 360^\circ - 60^\circ = 300^\circ\]

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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