In the given diagram, a circle is inscribed in a right angled triangle such that AF = 6 cm and EC = 15 cm. Find the difference between CD and BD.

1 cm

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3 cm

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4 cm

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2 cm

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Solution

The correct option is A
1 cm

As the lengths of tangents drawn from an external point to a circle are equal

AF = AE = 6

CE = CD = 15

Let BF = BD = x

Applying Pythagoras theorem to the above figure

${(6 + x)}^{2} + {(6 + 15)}^{2} = {(15 + x)}^{2}$

$36 + x^{2} + 12 x + 441 = 225 + x^{2} + 30 x$

$18 x = 252$

$x = 14$

Difference between CD and BD = 15 – 14 = 1 cm

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