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) cm^2

11.44 cm^2

Step-by-step explanation:

ABC is right angled triangle

BC^2 = AB^2 + AC^2

referring picture data

BC^2 = 6^2 + 8^2

BC = 10 cm

area of triangle abc

(1/2)*6*8 = 24 cm^2

let say radius of circle = r

then area of triangle

= (1/2)*6*r + (1/2)*8*r + (1/2)*10*r

= 12r

12r = 24

r = 2

area of circle = πr^2 = 4π cm^2

area of shaded region = (24 - 4π) cm^2

11.44 cm^2