IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

nadeemoidu

Find the least perimeter of the isosceles triangle in which a circle of radius r can be inscribed?
I would like to know what should be taken as variable to express the perimeter as a function .

gcch29

let the equal sides be       'a'             angle opp. to side 'a'      be A
let third side be 'b'              angle opp to 'b'        pi-2A
P=2a+b                 -----------(1)
inradius = r=(s-a)tanA/2                                     2s =2a+b
                r=(s-b) tan(pi - 2A)/2
from here calculate a & b
and put in (i)
from this we will get eqn in two variables(P & A)    & then use principal of maxima & minima

nadeemoidu

Actually i had thought of some method like that , just take half the angle between the equal sides as theta and all sides can be expressed in terms of theta and 'r'.

But that method was complicated , so I wanted to know if taking some other variable would make it easy.

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