A point P is 13 cm from the centre of the circle. The length of the tangent draw

Question

A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.

Options:

A . 10 cm

B . 5 cm

C . 7 cm

D . 12 cm

Answer: Option B
:
B

Since,
tangent to a circle is perpendicular to the radius through the point of contact
So,

∠ O T P = 90^{0}

So, in triangle OTP

(O P)^{2} = (O T)^{2} + (P T)^{2}

13^{2} = (O T)^{2} + 12^{2}

(O T)^{2} = 13^{2} - 12^{2}

O T^{2} = 25

O T = \sqrt{25}

O T = 5

So, radius of the circle is 5 cm

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