Asked in: July 2025 board paper In the following figure, point O is the centre of the circle and length of chord AB is equal to the radius of the circle. Find the measures of (i) ∠ AOB (ii) arc AB (iii) ∠ ACB, by completing the activity. Activity: In Δ AOB, AO = OB = AB therefore Δ AOB is an ____ triangle. therefore m∠ AOB = ____. m∠ AOB = m(arc AB) = ____ (definition of measure of an arc). m∠ ACB = 1/2 × ____ (inscribed angle theorem) = 1/2 × 60^° therefore m∠ ACB = ____ [Figure: circle with centre O; chord AB equal to the radius; C is a point on the major arc.]

Answer: (i) ∠ AOB = 60^° (ii) m(arc AB) = 60^° (iii) ∠ ACB = 30^° In Δ AOB, AO = OB = AB (radii and the given chord) therefore Δ AOB is an equilateral triangle. therefore m∠ AOB = boxed60^° (each angle of an equilateral triangle). m(arc AB) = m∠ AOB = boxed60^° (definition of measure of a minor arc). m∠ ACB = 1/2 × boxedm(arc AB) = 1/2 × 60^° = boxed30^° (inscribed angle theorem).

Chapter: Circle· Mathematics Part 2 (Geometry)

Asked in: July 2025 board paperIn the following figure, point O is the centre of the circle and length of chord AB is equal to the radius of the circle. Find the measures of (i) \(\angle AOB\) (ii) arc AB (iii) \(\angle ACB\), by completing the activ…

Asked in: July 2025 board paper

In the following figure, point O is the centre of the circle and length of chord AB is equal to the radius of the circle. Find the measures of (i) \(\angle AOB\) (ii) arc AB (iii) \(\angle ACB\), by completing the activity.

Activity: In \(\Delta AOB\), AO = OB = AB \(\therefore \Delta AOB\) is an ____ triangle. \(\therefore m\angle AOB = \) ____. \(m\angle AOB = m(\text{arc AB}) = \) ____ (definition of measure of an arc). \(m\angle ACB = \dfrac{1}{2} \times \) ____ (inscribed angle theorem) \(= \dfrac{1}{2} \times 60^\circ\) \(\therefore m\angle ACB = \) ____

[Figure: circle with centre O; chord AB equal to the radius; C is a point on the major arc.]

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Answer: (i) \(\angle AOB = 60^\circ\) (ii) m(arc AB) = \(60^\circ\) (iii) \(\angle ACB = 30^\circ\)

In \(\Delta AOB\), AO = OB = AB (radii and the given chord) \(\therefore \Delta AOB\) is an equilateral triangle.

\(\therefore m\angle AOB = \boxed{60^\circ}\) (each angle of an equilateral triangle).

\(m(\text{arc AB}) = m\angle AOB = \boxed{60^\circ}\) (definition of measure of a minor arc).

\(m\angle ACB = \dfrac{1}{2} \times \boxed{m(\text{arc AB})} = \dfrac{1}{2} \times 60^\circ = \boxed{30^\circ}\) (inscribed angle theorem).

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Asked in: July 2025 board paperIn the following figure, point O is the centre of the circle and length of chord AB is equal to the radius of the circle. Find the measures of (i) \(\angle AOB\) (ii) arc AB (iii) \(\angle ACB\), by completing the activ…

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