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प्रश्न
In figure, 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.
- ∠AOB
- ∠ACB
- arc AB
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उत्तर
i. seg OA = seg OB = radius ...(i) [Radii of the same circle]
seg AB = radius ...(ii) [Given]
∴ seg OA = seg OB = seg AB ...[From (i) and (ii)]
∴ ∆OAB is an equilateral triangle.
∴ m∠AOB = 60° ...[Angle of an equilateral triangle]
ii. `m∠ACB = 1/2 m∠AOB` ...[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]
∴ `m∠ACB = 1/2 xx 60^circ`
∴ m∠ACB = 30°
iii. m(arc AB) = m∠AOB ...[Definition of measure of minor arc]
∴ m(arc AB) = 60°
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