Tangent Perpendicular to Radius at Point of Contact
The length of...
Question
Question 6 The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
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Solution
AB is a tangent drawn on this circle from point A. ∴OB⊥AB OA = 5cm and AB = 4 cm (Given) In Δ ABO, By Pythagoras theorem in Δ ABO, OA2=AB2+BO2 ⇒52=42+BO2 ⇒BO2=25−16 ⇒BO2=9 ⇒BO=3 ∴ The radius of the circle is 3 cm.