Question

in ∆ABC AC+BC=28,AB+BC=32 and AC+AB=36 the determine the type of ∆ABC

Answer 1



Consider ABC be the right angled triangle such that ∠A = 90° and AB = 5cm, AC = 12 cm. 

And O be the centre and r be the radius of the incircle.

AB, BC and CA are tangents to the circle at P, N and M.

∴ OP = ON = OM =  r  (radius of the circle)

Area of ΔABC = ½ × 5 × 12 = 30 cm2

By Pythagoras theorem,

 BC2  = AC2  + AB2

 ⇒ BC2  = 122  + 52

⇒ BC2  = 169

⇒ BC = 13 cm

Area of ∆ABC = Area ∆OAB + Area ∆OBC + Area ∆OCA

30 = 1 2 r × AB + 1 2 r × BC + 1 2 r × CA 

30 = 1 2 r(AB+BC+CA)

⇒ r = 2 × 30 (AB+BC+CA) 

⇒ r = 60 5+13+12 

⇒ r = 60/30 = 2 cm.