A circle is inscribed in a ∆ ABC 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 :

For a triangle with sides 16 cm, 20 cm, 24 cm and an inscribed circle, the tangents from each vertex to the circle are equal. Let the tangent lengths be x, y, z from vertices A, B, C respectively. Then x+y = 16, y+z = 20, x+z = 24. Solving: Adding all three: 2(x+y+z) = 60, so x+y+z = 30. Therefore x = (x+y+z) - (y+z) = 30 - 20 = 10 cm. AD is the tangent from A, which equals x = 10 cm (option A).