Q4 of 26 Page 235

A triangle ABC is drawn to circumscribe a circle of radius 3 cm. such that the segments BD and DC into which BC is divided by the point of contact D are of length 9 cm. and 3 cm. respectively (See adjacent figure). Find the sides AB and AC.


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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