Q. 34.0( 5 Votes )

The length of tangent from a point A at a distance of 5 cm from the center of the circle is 4 cm. What is the radius of the circle?

Answer :

Given:


OA (say) = 5 cm


AB = 4 cm



Let AC be the tangent which meets the circle at the point B and O be the center of circle.


Property: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.


By above property, ∆AOB is right-angled at OBA.


Therefore, by Pythagoras Theorem,


AB2 + OB2 =AO2


OB 2 = AO2 – AB2


OB= √(AO2 – AB2)


OB= √(52 – 42)


OB= √(25 – 16)


OB = √9


OB= 3 cm


Hence, Radius = 3 cm


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