CAT 2024 Geometry & Mensuration Question (Hard)

Question

A circular plot of land is divided into two regions by a chord of length meters such that the chord subtends an angle of at the center. Then, the area, in square meters, of the smaller region is

Accepted Answer

Step 1 We are given a circle with center , and a chord of length meters that subtends an angle of at the center. So, , and radii of the circle . Then, triangles is isosceles, and Draw perpendicular from to chord . Step 2 Use right triangle to find the radius . Image ! Circle with chord https optima-

CAT 2024

Quantitative

Geometry & Mensuration

Hard

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

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