Question
A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.
Answer: Option B
:
B
Given that AO = AB=OB.
Since all sides are equal, △AOB is equilateral, and hence equiangular. Also, each angle of the triangle equals 60∘.
i.e.,∠AOB = 60∘
⟹∠ACB=12AOB
(∵ Angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.)
⟹∠ACB=60∘2=30∘
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:
B
Given that AO = AB=OB.
Since all sides are equal, △AOB is equilateral, and hence equiangular. Also, each angle of the triangle equals 60∘.
i.e.,∠AOB = 60∘
⟹∠ACB=12AOB
(∵ Angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.)
⟹∠ACB=60∘2=30∘
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