Question

In figures 3.56 in a circle with center o length of chord AB is equal to the radius of the circle find measure of each of the following .​

Answer 1

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The measure of an angle subtended by an arc at a point on the circle is half of the measure of the angle subtended by the arc at the centre. Thus, the measure of ∠ACB is 30º. Thus, the measure of arc AB is 60º. Thus, the measure of arc ACB is 300º.

Answer 2

Answer:

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(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°