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Lengths of Tangents Drawn from External Point

In the given ...

Question

In the given figure, $△$ ABC is circumscribed. The circle touches the sides AB, BC and CA at P, Q, R respectively. If AP = 5 cm, BP = 7 cm, AC = 14 cm and BC = $x$ cm, find the value of $x$ .

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Solution

AR = AP = 5 cm

RC = AC – AR = 14 – 5 = 9

QC = RC = 9

BQ = BP = 7

BC = BQ + QC = 7 + 9 = 16 cm

Therefore the value of $x$ = 16 cm

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