In a right triangle abc right angled at b

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In a right angle triangle ABC, right angled at B, BC=5cm and AB=12 CM. the circle is touching the sides of triangle ABC .Find the radius of the circle. (pls explain with diagram.)

Answered by admin @


Step-by-step explanation:

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 cm^2


By Pythagoras theorem,

 BC^2  = AC^2  + AB^2

 ⇒ BC^2  = 12^2  + 5^2


⇒ 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.


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