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.

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.

Explanation:

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
CA=6+7=13
cm

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