Q. 254.0( 2 Votes )

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 :

Given: area of ΔABC is 84 cm2.

To find: The length of AB and AC.

Theorem Used:

The length of two tangents drawn from an external point are equal.


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

C is an external point and CF and CD are the tangents drawn from it.

CF = CD=6cm

Similarly, BE = BD =8cm (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 heron’s formula

Squaring both side and solving we get,
x(x+14)-7(x+14) =0
or x=-14and7
x=-14 is not possible
so x=7
hence AB=7+8=15cm

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