Question

A circle is inscribed in a triangle abc having sides 8cm 10cm and 12cm find ad be and cf

Answer 1

Answer:

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