Q. 43.9( 23 Votes )

# A triangle ABC is

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 + x2 = 144 + 9 + 6x + x2

12x = 72

X = 6cm

AB = 9 + 6 = 15cm

AC = 6 + 3 = 9cm

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