Answer :

Construction : Draw radius OB = 3cm

Proof: AC, BC and AB are tangents

BF = BD = 9cm—tangents from B

AF = AB—tangent from A

∴ CD = CB tangents from C

OD = OB = 3cm radius

OBCD forms a square of side 3cm

OD = OB = BC = CD = 3cm

∴ ∠BCD = 90°

BD = 9cm and DC = 3cm

OB = 3cm radius of circle

Let AF = AB = x

Applying Pythagoras

AB = BC + AC

(9 + x)^{2} = (12)^{2} + (3 + x)^{2}

81 + 18x + x^{2} = 144 + 9 + 6x + x^{2}

12x = 72

X = 6cm

∴ AB = 9 + 6 = 15cm

AC = 6 + 3 = 9cm

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