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.
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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