Q. 33 5.0( 3 Votes )

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.


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



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