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:

25 cm 33 cm 23 cm 20 cm

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