Question

A cicle inscribed in a triangle ABC having side BC = 8cm AC = 10cm AB = 12cm find AD, BE and CF

Answer 1

Tangents drawn from an external point to a circle are equal.
⇒ AD = AF, BD = BE, CE = CF.

Let AD = AF = a
BD = BE = b
CE = CF = c

AB = AD + DB = a + b = 8 -------- (1)
BC = BE + EC = b + c = 10 -------- (2)
AC = AF + FC = a + b = 12 -------- (3)

Adding (1), (2) and (3), we get
2 (a + b + c) = 30
⇒ (a + b + c) = 15 -------- (4)

Subtracting (1) from (4), we get c = 7
Subtracting (2) from (4), we get a = 5
Subtracting (3) from (4), we get b = 3

Therefore, AD = a = 5 cm, BE = b = 3 cm, CF = c = 7 cm