Question

A circle is inscribed in ∆ABC having sides 8 cm, 10 cm and 12 cm as shown in the figure, Find AD, BE and CF.

Answer 1

AD = AF = x   ...(Tangent of the circle)

BD = BE = y   ...(Tangent of the circle)

CE = CF = z   ...(Tangent of the circle)

AB = AD + DB

x + y = 12   ...(1)

BC = BE + EC

y + z = 8   ...(2)

AC = AF + FC

x + z = 10  ...(3)

Add (1), (2) and (3)

2x + 2y + 2z = 12 + 8 + 10

x + y + z = `30/2` = 15  ...(4)

By x + y = 12 in (4)

z = 3

y + z = 8 in (4)

x = 7

x + z = 10 in (4)

y = 5

AD = 7 cm, BE = 5 cm and CF = 3 cm