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A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle. - Mathematics

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Sum

A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.

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Solution

Since tangent to a circle is perpendicular to the radius through the point of contact.

∴ ∠OTP = 90°

In right triangle OTP, we have

`OP^2 = OT^2 + P^2`

`⇒ 13^2 = OT^2 + 12^2`

`⇒ OT^2 = 13^2 – 12^2`

= (13 – 12) (13 + 12) = 25

⇒ OT = 5

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
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