Question

If in a right angled triangle ABC, angle B = 90 degree, AC = 10 cm and radius of incircle is 1 cm, then the perimeter of the triangle is ?

Answer 1

Draw perpendicular from Incenter O on to AB, BC and AC, meeting them at D, E and F  respectively. 
BD = BE = incircle radius = 1 cm, as it is a square.

Let CE = CF = x cm

AF = 10 - x   => AD = 10 -x 

Pythagoras theorem =>   (10-x +1)^2 + (1+x)^2 = 10^2
       x^2 - 10 x + 11 = 0
 x = 5 + sqroot(14)   or 5 - sqroot(14)

Then  AB = 6 - sqroot(14),       BC = 6 + sqroot(14),  or the otherway round.

Perimeter =  22 cm