CAT 2017 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Geometry Questions | Question 17

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Question 17 : Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq. cm, of the region enclosed by BPC and BQC is :

  1. 9π - 18
  2. 18
  3. 9

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Explanatory Answer

Method of solving this CAT Question from Geometry
CAT 2017 Question Paper Quants Slot 1 Geometry

Given that ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC and let BPC be an arc of a circle centred at A and lying between BC and BQC.
If AB has length 6 cm then the area, in sq. cm, of the region enclosed by BPC and BQC has to be found.
i.e. the shaded region is,
Area of semicircle BQC = π (3√(2))2
= \\frac{18π}{2})
= 9π
Area of BPC = \\frac{π}{4}) × 62 - Area of triangle
= 9π - 9π - 18
= 18

The question is "Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq. cm, of the region enclosed by BPC and BQC is :"

Hence, the answer is 18

Choice B is the correct answer.

 

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