CAT 2022 Question Paper | Quant Slot 3

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 18 : In a triangle $\mathrm{ABC}, \mathrm{AB}=\mathrm{AC}=8 \mathrm{cm}$. A circle drawn with $\mathrm{BC}$ as diameter passes through $\mathrm{A}$. Another circle drawn with center at A passes through B and $\mathrm{C}$. Then the area, in sq. $\mathrm{cm}$, of the overlapping region between the two circles is

Video Explanation

Explanatory Answer

AB = AC = 8cm
Since BC is the diameter, angle A has to right-angled and angle B = angle C = 45 degrees.
Therefore, the radius of the circle centred at O is $4 \sqrt { 2 }$.
The radius of the circle centred at Aa is 8cm.
The common area between them = (half of the smaller circle) + (and the minor segment created by the chord BC in the bigger circle)
= $\frac { 1 } { 2 } \pi ( 4 \sqrt { 2 } ) ^ { 2 }$ + (Ar(sector AOB) - Ar(AOB))
= $16 \pi$ + (Ar(sector AOB) - Ar(AOB))
= $16 \pi$ + ($\frac { 1 } { 4 } \pi ( 8 ) ^ { 2 }$ - $\frac { 1 } { 2 } * 8 * 8$)
= $16 \pi + 16 \pi - 32$
= $32 \pi - 32$
= $32 ( \pi - 1 )$

The answer is '$32(\pi-1)$'

Choice B is the correct answer.

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