Mathematics
A point P is 17 cm away from the centre of the circle and the length of the tangent drawn from P to the circle is 15 cm. Find the radius of the circle.
Circles
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Answer
Consider a circle with centre O,
Let P be an external point from where a tangent is drawn to meet the circle at A.
∴ OP = 17 cm and AP = 15 cm
We know that,
The tangent at any point of a circle and the radius through this point are perpendicular to each other.
In right angled ∆OAP, we have
⇒ OP2 = OA2 + AP2
⇒ 172 = OA2 + 152
⇒ 289 = OA2 + 225
⇒ OA2 = 289 - 225
⇒ OA2 = 64
⇒ OA =
⇒ OA = 8 cm
Hence, the radius of circle is 8 cm.
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