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Abc is right angled triangle at b then find the diameter of incircle of triangle

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Raghunath answered 3 year(s) ago

ABC is a right angled triangle, right angled at A. a circle is inscribed in it. the length of two sodes containing angle A is 12 cm and 5 cm. find the radius.

Class-IX Maths

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Asked by Anoop

Feb 18

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Raghunath , SubjectMatterExpert

Member since Apr 11 2014



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.