A circle inscribed in a triangle ABC touches its sides AB, BC and AC at the points D, E and F, respectively. If AB = 18 cm, BC = 15 cm and AC = 13 cm, then the value of AD + BE + CF is:

23 cm

We have,

AB = 18

BC = 15

AC = 13

We know,

 AD = AF, DB = BE, CE = FC

The perimeter of the triangle  = 18 + 15 + 13 = 46

= AD + AF + BD + BE + CE + CF = 46

= 2 × (AD + BE + CF) = 46

= (AD + BE + CF) = 23 cm