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.

(1)In ∆AOB,

AB = OA = OB = radius of circle

⇒ ∆AOB is an equilateral triangle

∠ AOB + ∠ ABO + ∠ BAO = 180° {Angle sum property}

⇒ 3∠ AOB = 180° {All the angles are equal}

∠ AOB = 60°

(2)∠ AOB = 2 × ∠ ACB {The measure of an inscribed angle is half the measure of the arc intercepted by it.}

⇒∠ ACB = 30°

(3)∠ AOB = 60°

⇒arc(AB) = 60° {The measure of a minor arc is the measure of its central angle.}

(4) Using Measure of a major arc = 360°- measure of its corresponding minor arc

⇒arc(ACB) = 360° - arc(AB)

⇒arc(ACB) = 360° - 60° = 300°