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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Question : The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is:
Option 1: $75^{\circ}$
Option 2: $60^{\circ}$
Option 3: $150^{\circ}$
Option 4: $120^{\circ}$
Question : The chord of a circle is equal to its radius. Find the difference between the angle subtended by this chord at the minor arc and the major arc of the circle.
Option 1: 30°
Option 2: 120°
Option 3: 60°
Option 4: 150°
Question : A chord of length 7 cm subtends an angle of $60^{\circ}$ at the centre of a circle. What is the radius (in cm) of the circle?
Option 1: $7\sqrt{2}$ cm
Option 2: $7\sqrt{3}$ cm
Option 3: $7$ cm
Option 4: $14$ cm
Question : If a chord of length 16 cm is at a distance of 15 cm from the centre of the circle, then the length of the chord of the same circle which is at a distance of 8 cm from the centre is equal to:
Option 1: 10 cm
Option 2: 20 cm
Option 3: 30 cm
Option 4: 40 cm
Question : A chord of length 120 cm is at a distance of 32 cm from the centre of a circle. What is the radius (in cm) of the circle?
Option 1: 96
Option 2: 34
Option 3: 72
Option 4: 68
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