CAT 2018 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Geometry Questions | Question 8

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

  1. 5√3
  2. 6√2
  3. 8

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Explanatory Answer

Method of solving this CAT Question from Geometry
CAT 2018 Question Paper Quants Slot 2 Geometry

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"

Hence, the answer is 5√3

Choice B is the correct answer.

 

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