A circle is inscribed in the triangle ABC whose sides are given as AB = 10, BC = 8, CA= 12 units as shown in the figure. The value of AD × BF is:

18 units 21 units 16 units 15 units

21 units

We have, AB = 10, BC = 8, CA= 12 Semi Perimeter of the triangle = \(\frac{10 + 8 + 12}{2}\) = 15 Now the value of AD = 15 - BC = 15 - 8 = 7 And the value of BF = 15 - AC = 15 - 12 = 3 So, the value of AD × BF = 7 × 3 = 21 units