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Question

A chord AB 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 and minor arc respectively .

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Solution


In ΔOAB,
AB = OA = OB = radius
ΔOAB is an equilateral triangle.
Therefore, each interior angle of this triangle will be of 60.
AOB=60.
ACB=12AOB=12(60)=30
In cyclic quadrilateral ACBD,
ACB+ADB=180 (Opposite angle in cyclic quadrilateral are supplementary)
ADB=18030=150
Therefore, angle subtended by this chord at a point on the major arc and the minor arc are 30 and 150 respectively.

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