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The length of a tangent from …

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The length of a tangent from a point A at distance 5cm from the centre of the circle is 4cm. Find the radius of the circle.

Posted by Pihu ✨ 4 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Kiran Chaudhri 4 years, 8 months ago

Let AT be the tangent drawn from a point A to a circle with centre O and OA=5 cm and AT=4 cm. Since tangent at a point is perpendicular to the radius through the point of contact ∴OT⊥AT ∴ from right angled △OAT, (OA)2=(OT)2+(TA)2 ⇒(5)2=(OT)2+(4)2 ⇒25−16=(OT)2 ⇒9=(OT)2 ⇒OT=3 cm ∴ radius of the circle =3 cm.

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