CAT 2024 Slot 3 QA Question 13: A circular plot of land is divided into two regions by a chord of length $10\sqrt{3}$ meters such that the chord subtends an angle of $120^\circ$ at the center. Then, the area, in square meters, of th

Question

A circular plot of land is divided into two regions by a chord of length $10\sqrt{3}$ meters such that the chord subtends an angle of $120^\circ$ at the center. Then, the area, in square meters, of th

Accepted Answer

Let the radius of the circle be $R$. The chord subtends $120^\circ$ at the centre, so half the angle is $60^\circ$.

$	ext{Chord length} = 2R\sin 60^\circ$
$10\sqrt{3} = 2R	imes \dfrac{\sqrt{3}}{2}$
$10\sqrt{3} = R\sqrt{3}$
$R = 10$

The smaller region is the minor segment cut off by the chord.

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A circular plot of land is divided into two regions by a chord of length 10310\sqrt{3}103​ meters such that the chord subtends an angle of 120∘120^\circ120∘ at the center. Then, the area, in square meters, of the smaller region is

A circular plot of land is divided into two regions by a chord of length $10\sqrt{3}$ meters such that the chord subtends an angle of $120^\circ$ at the center. Then, the area, in square meters, of the smaller region is