Find the length of the tangent drawn from a point whose distance from the centre of circle is 25 cm. Given that the radius of the circle is 7 cm.

20cm

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24cm

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28cm

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30cm

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Solution

The correct option is B
24cm

Since tangent at a point on the circle is perpendicular to the radius through the point.

$∴ ∠ O T P = 90^{\circ}$

In right angled triangle OTP

${O P}^{2} = {O T}^{2} + {P T}^{2}$ (By Pythagoras theorem)

$25^{2} = 7^{2} + {P T}^{2}$

$625 = 49 + {P T}^{2}$

${P T}^{2} = 625 - 49 = 576$

$P T = \sqrt{576} = 24$

Hence, length of tangent PT = 24 cm.

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A point P is 25 cm away from the centre of a circle and the length of tangent drawn from P to the circle is 24 cm. Find the radius of the circle.

Q

24 c m

25 c m

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