This question is from ** CAT** geometry. It discusses about a circular arc that has been drawn keeping a vertex of a triangle as a center. With the given data how can you find the area of the required region - Mr. Pythagoras might help you to start solving this problem! Give it a shot, and then watch the detailed video solution.

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 :

- 9π - 18
- 18
- 9π
- 9

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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}) × 6^{2} - 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 :" **

Choice B is the correct answer.

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