a circle is inscribed in a triangle ABC having sides AB=10 cm AC=8cm BC=12cm such that it touches AB at F AC at E and BC at D.

find AF , BD and CE

Question

a circle is inscribed in a triangle ABC having sides AB=10 cm
AC=8cm BC=12cm such that it touches AB at F AC at E and BC at D
find AF , BD and CE

Gursheen kaur. · Accepted Answer

Tangents drawn from an external point to a circle are equal

Let

AD = AF = x

BD = BE = y

and CE = CF = z

Now,

AB = AD + DB = x + y= 10 (1)

BC = BE + EC = y + z= 12 (2)

AC = AF + FC = x + y= 8 (3)

Adding (1), (2) and (3), we get,

â‡’2 (x+ y+ z) =
30

â‡’ (x+ y+ z) = 15
(4)

On Solving (1) and (4), we get, z =5

Solving (2) and (4), we get x = 3

Solving (3) and (4), we get y = 7

Hence,

AD = AF= x = 3 cm

BD = BE = y = 7 cm

CE =CF = z = 5 cm