A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm and AC = 24 cm, and side AB, BC and AC touches circle at D, E and F, respectively. The measure of AD is:

10 cm

As from point A two tangent is drawn on the circle

⇒ AD = AF = a

Similarly, from point B two tangent is drawn on the circle

⇒ BD = BE = b

Similarly, from point C two tangent is drawn on the circle

⇒ CE = CF = c

According to the question

⇒ AB = a + b

⇒ 16 = a + b     ..(1)

⇒ BC = b + c

⇒ 20 = b + c     ..(2)

⇒ AC = a+ c

⇒ 24 = a + c     ..(3)

Now, on adding eq (1), (2) and (3), we get

⇒ 16 + 20 + 24 = a + b + b + c + a + c

⇒ a + b + c = 30

Now put the value of b + c in above equation, we get

⇒ a + 20 = 30

⇒ a = 10 cm

Therefore, the value of AD is 10 cm.