Abc Is Triangle With Ab 10 Cm Bc 8 Cm And Ac 6 Cm Not Drawn To Scale

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale ). … vertices as their centres. Find the radii of the…

Answers:

AB  = 10 cm

BC = 8 cm

AC = 6 cm

Let the radii of three circle be r₁, r₂ & r₃  (shown in fig.)

 r₁ + r₂  = 10 = AB   ….(1)

r₂  + r₃ = 6 = AC    …..(2)

 r₃ + r₁ = 8 = BC    …..(3)

adding (1), (2) and (3), we get

2(r₁ + r₂ +  r₃) = 10 + 6 + 8 = 24

  r₁ + r₂ +  r₃  = 12      …..(4)

Subtract (4) and (1) ⇒ r₃  = 12 – 10 = 2 cm

Subtract (4) and (2) ⇒ r₁ = 12 – 6 = 6 cm

Subtract (4) and (3) ⇒  r₂ = 12 – 8 = 4 cm