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Question -

A chord of a circle is equal to the radius of the circle, find the anglesubtended by the chord at a point on the minor arc and also at a point on themajor arc.



Answer -

 Wehave a circle having a chord AB equal to radius of the circle.

∴ AO = BO = AB
⇒ ∆AOB is an equilateraltriangle.
Since, each angle of an equilateral triangle is 60°.
⇒ ∠AOB = 60°
Since, the arc ACB makes reflex ∠AOB= 360° – 60° = 300° at the centre of the circle and ∠ACB at a point on the minorarc of the circle.
Hence,the angle subtended by the chord on the minor arc = 150°.
Similarly,, ∠ADB= 1 [∠AOB] = 1 x60° = 30°
Hence, the angle subtended by the chord on the major arc = 30°

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