Question

In Fig. a ΔABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of ΔABC is 84 cm².

Answer 1

Firstly consider that the given circle will touch the given circle will touch the sides AB and AC of the triangle at a point E and F respectively.

Let AF = x

Now in triangle ABC

CF = CD = 6cm

(Tangent drawn from an external point to a circle are equal. 

Here tangent is drawn from external point C)

BE = BD = 8cm (Tangent drawn from an external point to a circle are equal. 

Here tangent is drawn from external point B)

AE = AF = X

Now AB = AE + EB = x + 8

Also BC = BD + DC = 8 + 6 = 14 

and CA = CF + FA = 6 + x

Now we get all side of the triangle and its area can be find by using hero’s formula