Three circles each of radius 5 cm touch one another. The area (in cm²) subtended between them.

Each side of the triangle formed by the centers of the circles is equal to the sum of the radii of two touching circles, which is 2 x 5 = 10 cm. The formula for the area of an equilateral triangle is- Area = (√3/4) a² Where s is the side length of the triangle. Here, a = 10 cm. A = √3/ 4 × 10² = 25√3 cm² Each sector is part of a circle with a radius of 5 cm, and since each angle at the centers is 60° (as the triangle is equilateral), the area of one sector is: Area of one sector =60°/360° × πr² =1/6 ×π ×5² =25π/6 cm² The total area of the three sectors is=3×25π/6 =25π/2 cm² The area between the circles is the area of the equilateral triangle minus the area of the three sectors: Area = 25√3 – 25 π /2 =25(√3 - π /2) Therefore, the area subtended between the three circles is: Area = 25 (√3- π /2) cm²