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

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#### Solution

Draw a circle and let P be a point such that OP = 25cm.

Let TP be the tangent, so that TP = 24cm

Join OT where OT is radius.

Now, tangent drawn from an external point is perpendicular to the radius at the point of contact.

∴ OT ⊥ PT

In the right Δ OTP,we have:

`OP^2 = OT^2 +TP^2 ` [By Pythagoras’ theorem:]

`OT^2 = sqrt(OP^2 - TP^2 )`

`=sqrt(25^2 - 24^2`

`= sqrt(625-576)`

`=sqrt(49)`

= 7 cm

∴ The length of the radius is 7cm.

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

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