Question

Abc is a right angled triangle at a find the area of shaded region

Answer 1

Answer:

Answer. ABC is a right angled triangle at right angled at A. BC = 10 cm, AB = 6 cm. Let ‘O’ be the centre and r be the radius of the incircle. AB, BC and CA are tangents to the circle at P, M and N. ∴ IP = IM = IN = r (radius of the circle) In right ΔBAC, BC2 = AB2 + AC2 [Pythagoras theorem,] ⇒ 102 = 62 + AC2 ⇒ AC2 = 100 - 36 ⇒ AC2 = 64 ⇒ AC = √64 = 8 cm Area of ∆ ABC = 1/2 × base × height = 1/2 × AC × AB = 1/2 × 8 × 6 = 24 cm2 Area of ∆ABC = Area ∆IAB + Area ∆IBC + Area ∆ICA ⇒ 24 = 1/2 r (AB) + 1/2 r (BC) + 1/2 r (CA) = 1/2 r (AB + BC + CA) = 1/2 r (6 + 8 + 10) = 12 r r = 2 Area of the circle = πr2 = 3.14 x 2 x 2 = 12.56 cm2 Area of shaded region = Area of ∆ABC - Area of circle = 24 – 12.56 = 11.44 cm2. Hence, the area of the shaded region is 11.44 cm2.