Question : A chord of a circle is equal to its radius of length 9 cm. Find the angle subtended by it in the major segment.
Option 1: $90^\circ$
Option 2: $60^\circ$
Option 3: $30^\circ$
Option 4: $120^\circ$
Correct Answer: $30^\circ$
Solution :
The length of the chord(AB) = radius(OB) = 9 cm
When the length of the chord and the radius are equal, the triangle formed is equilateral.
The angles of an equilateral triangle are $60^\circ$
$\therefore$ The angle subtended in the major segment is half of the angle subtended at the centre.
Angle at the major segment subtended by the chord = $\frac{60^\circ}{2}$
= $30^\circ$
Hence, the correct answer is $30^\circ$.
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