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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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asked May 14, 2017 in Mathematics by sforrest072 (157,439 points) ● 60 ● 409 ● 933
retagged May 14, 2017 by sforrest072

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answered May 14, 2017 by vikash (21,277 points) ● 4 ● 19 ● 70
selected May 14, 2017 by sforrest072
 
Best answer

Solution:

AB is a tangent drawn on this circle from point A.

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.

∴ OB ⊥ AB
OA = 5cm and AB = 4 cm (Given)
In ΔABO,
By Pythagoras theorem in ΔABO,
OA2 = AB2 + BO2
⇒ 52 = 42 + BO2
⇒ BO2 = 25 - 16
⇒ BO2 = 9
⇒ BO = 3
∴ The radius of the circle is 3 cm.

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