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the below given figure, a triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the segments BD and DC are respectively of lengths 6 cm and 9 cm. If the area of ΔABC is 54 cm^{2}, then find the lengths of sides AB and AC.

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#### Solution

**Given : **OD = 3cm**Construction : **Join OA, OB and X

**Proof :**Area of the ΔABC = area of ΔOBC + area of ΔOAC + arc of ∠ OAB.

BD = 6 cm : BE = 6 cm ( equal tangents )

DC = 9 cm : CF = 9 cm ( equal tangents )

AB = AF + FB = 6 + x = 6 + 3 = 9.

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