Question

the length of tangent to a circle which is 13cm distance from the centre of the circle is 12cm find the radius of the circle
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Answer 1

Radius of circle = 5 cm if the length of tangent to a circle which is 13cm distance from the centre of the circle is 12cm

Step-by-step explanation:

Let say Cenetr of circle = O

Tangent PA is drawn from point P touching circle at A

OP = 13 cm  ( Distance of point from center of Circle)

PA = 12 cm  ( Length of Tangent)

OA = Radius = ?

Applying Pythagorean theorem

OP² = PA² + OA²

=> 13² = 12² + Radius²

=> 169 = 144 + Radius²

=> Radius² = 25

=> Radius² = 5²

=> Radius = 5 cm

Radius of circle = 5 cm

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Answer 2

Answer:

13^2 = 12^2 + r^2

169–144 = r^2

r^2 = 25

r = 5

Step-by-step explanation:

radius is perpendicular to the tangent line at the tangent point, the three lines form a right triangle. The hypotenuse is 13, one side is 12 and the radius is the third side. By the Pythagorian theorem, the radius is 5.