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

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

Team Careers360 · Accepted Answer

Correct Answer: $7$ cm

Solution :
Since a chord subtends the angle at the centre, the other angles of the triangle formed by the chord and the centre will be the same as two sides opposing. It will be the same because both are radii of the circle.
Let the other two angles be x.
We know that,
The sum of the angles of the triangle = 180$^\circ$
⇒ 60$^\circ$ + x + x = 180$^\circ$
⇒ 2x = 120$^\circ$
⇒ x = 60$^\circ$
$ herefore$ All angles are 60$^\circ$ (equilateral triangle)
$ herefore$ Radius of triangle = side of triangle = 7 cm
Hence, the correct answer is $7$ cm.

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Question : A chord of length 7 cm subtends an angle of 60∘ at the centre of a circle. What is the radius (in cm) of the circle?Option 1: 72 cmOption 2: 73 cmOption 3: 7 cmOption 4: 14 cm

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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