Question

From a point Q, the length of the tangent to a circle is 7 cm and the distance of Q from the centre is 25 cm. The radius of the circle is​

Answer 1

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From a point Q, the length of the tangent to a circle is 7 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

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Given:

• Tangent = xy

• Tangent = xyPoint of contact = b

• Tangent = xyPoint of contact = bLength of tangent of circle = 7cm

• Tangent = xyPoint of contact = bLength of tangent of circle = 7cmi.e PQ = 7cm

• Tangent = xyPoint of contact = bLength of tangent of circle = 7cmi.e PQ = 7cmOQ = 25cm

Tangent = xyPoint of contact = bLength of tangent of circle = 7cmi.e PQ = 7cmOQ = 25cm_______________________________

To find:

• Radius of the circle

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Solution:

Since XY is tangent

OP ⟂ XY ( Tangent at any point of circle is perpendicular to the radius through point of contact)

$so \: ∠OPQ = 90°$

So △OPQ is a right angled triangle

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$\large{\underline{\sf{\blue{Using\: Pythagoras\:theorem:}}}}$

${OQ}^{2} = {OP}^{2} + {PQ}^{2}$

${(25)}^{2} = {(OP)}^{2} + {(7)}^{2}$

${OP}^{2} = {25}^{2} - {7}^{2}$

${OP}^{2} = 625 - 49$

${OP}^{2} = 576$

$op = 24cm$

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