In ∆ A B C , suppose the radius of the circle opposite to angle A is denoted by r 1 , similarly r 2 ↔ angle B , r 3 ↔ angle C . If r 1 = 2 , r 2 = 3 , r 3 = 6 , then what is ( a , b , c ) =

Step-by-step solution

Given, in ∆ A B C ,   r 1 = 2 , r 2 = 3 , r 3 = 6 To find: a ,   b ,   c = ? r 1 = ∆ s - a , r 2 = ∆ s - b , r 3 = ∆ s - c s - a = ∆ 2 , s - b = ∆ 3 , s - c = ∆ 6 Adding all, 3 s - ( a + b + c ) = ∆ 2 + ∆ 3 + ∆ 6 ⇒ 3 s - 2 s = 6 ∆ 6 ⇒ s = ∆       . . . . . . ( i ) As we know ∆ = s ( s - a ) ( s - b ) ( s - c ) ⇒ ∆ = ∆ ∆ 2 ∆ 3 ∆ 6 ⇒ ∆ = ∆ 2 6 &#