Question

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A triangle ABC is drawn to circumscribe a circle of radius 4cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8cm and 6cm respectively (see Fig.10.14). Find the sides AB and AC.​

Answer 1

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To Prove :

»» Side AB = ? and Side AC = ? BD = 8 cm. DC = 6 cm. BE = 8 cm. CF = 6 cm. AE = AF = x cm. In ∆ABC, a = BC = BD + DC =8 + 6 =14 cm. b = CA = (x + 6) cm. c = AB = (x + 8) cm.««

Remaining Process In The Attachment.

»» 48x × (x + 14) = 16 x (x + 14)2 3x = x + 14 ∴ x = 7 cm. AB = c = x + 8 = 7 + 8 = 15 cm. AC = b = x + 6 = 7 + 6 = 13 cm.««

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Answer 2

Answer:

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$\:$ AB = 15cm

AC = 13cm