In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 4 cm and 3 cm respectively. If the area $Δ$ ABC = 21 $c m^{2}$ then find the lengths of sides AB and AC.

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Solution

The sides AB, BC and CA are tangent to the incircle of ΔABC.

We know that, the length of tangent drawn from an external point of the circle are equal.

∴ CF = CD = 3 cm

BF = BD = 4 cm.

AF = AE = x cm (Say)

∴ AC = AF + CF = (x + 3) cm

AB = AE + BE = (x + 4) cm

Radius of the incircle, r = 2 cm (Given)

Area of ΔOBC + Area of ΔAOB + Area of ΔAOC = Area of ΔABC

AB = (x + 4) cm = (3.5 + 4) cm = 7.5 cm

AC = (x + 3) cm (3.5 + 3) cm = 6.5 cm

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