This is a classic question from **Geometry ** part of the **Quantitative Ability** of the **CAT exam** that appeared in the slot 2 of the CAT 2018 Question paper. Try this piece-of-a-cake question before having a look at the video solution. To solve more CAT-Level questions with detailed video solutions, please visit: **CAT Previous Year Paper**

Question 8 : A chord of length 5 cm subtends an angle of 60° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120° at the centre of the same circle is

- 2π
- 5√3
- 6√2
- 8

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Given that a chord of length 5 cm subtends an angle of 60° at the centre of a circle.

We have to find the length of a chord that subtends an angle of 120° at the centre of the same circle

sin 60° = \\frac{BC}{OB})

⟹ \\frac{√3}{2}) = \\frac{BC}{5})

⟹ BC = \\frac{5√3}{2}) and AC = \\frac{5√3}{2})

So AB = \\frac{5√3}{2}) + \\frac{5√3}{2}) = 5√3

The length of a chord that subtends an angle of 120° at the centre of the same circle is 5√3

The question is **"A chord of length 5 cm subtends an angle of 60° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120° at the centre of the same circle is"**

Choice B is the correct answer.

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