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

- \(16(\pi-1)\)
- \(32(\pi-1)\)
- \(32 \pi\)
- \(16 \pi\)

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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))

= \( 16 \pi \) + (\( \frac { 1 } { 4 } \pi ( 8 ) ^ { 2 } \) - \( \frac { 1 } { 2 } * 8 * 8 \))

= \( 16 \pi + 16 \pi - 32 \)

= \( 32 \pi - 32 \)

= \( 32 ( \pi - 1 ) \)

Choice B is the correct answer.

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