Question

∆ABC is right angled at A. The sides AB,BC and AC are the tangents to the circle with center O as shown in the figure . If AB=6CM,BC=8CM,find the area of the shaded region​

Answer 1

Answer:

24 - 4π cm²

11.44 cm²

Step-by-step explanation:

Taking Question data as per picture

AB = 6 cm  ,  AC = 8 cm

BC = √AB² + AC² = √6² + 8² = √100 = 10 cm

Area of Triangle ABC = (1/2) AB * AC = (1/2) * 6 * 8 = 24 cm²

Area of Triangle ABC = Area of Δ AOB + Area of Δ AOC + Area of Δ BOC

r = Radius of Circle

Area of Δ AOB = (1/2) * AB * r

Area of Δ AOC = (1/2) * AC * r

Area of Δ BOC = (1/2) * BC * r

=>24 = (1/2) * AB * r + (1/2) * AC * r + (1/2) * BC * r

=> 48 = (AB + AC + BC) * r

=> 48 = (6 + 8 + 10) * r

=> 48 = 24 r

=> r = 2

Radius = 2cm

Area of Circle = πr² = π2² = 4π cm²

Area of Shaded region = 24 - 4π cm² = 11.44 cm²