Question

a point P is 13 cm from the centre of the circle the length of the tangent drawn from the P of the circle is 12 cm find the radius of the circle​

Answer 1

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Answer 2

$\bf\huge\boxed{\boxed{\boxed{Solution:-}}}$

Given,

• AP = 12 cm
• OP = 13 cm

To find : Radius, OA

Now

We know that the tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.

Here, AP is the tangent and ∠OAP = 90°

Hence , applying Pythagoras theorem to ∆OAP,

${\implies{\sf{}}}$OP^2 = AP^2 + OA^2

${\implies{\sf{}}}$ 13^2 = 12^2 + OA^2

${\implies{\sf{}}}$ 169 = 144 + OA^2

${\implies{\sf{}}}$ OA^2 = 169 - 144

${\implies{\sf{}}}$ OA^2 = 25

${\implies{\sf{}}}$ OA =√25

${\implies{\sf{}}}$ OA = 5

Hence , the radius of the circle , OA is :-

$\huge{\boxed{\bold{5\:cm}}}$