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.
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Question

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.

KnowledgeBoat · Accepted 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.

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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