In Fig. 10.68, a 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 is 84 cm².

Question

In Fig. 10.68, a

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

is 84 cm².

Philoid · Accepted Answer

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

In Fig. 10.68, a 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 is 84 cm2.

In Fig. 10.68, a 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 is 84 cm².