Question

from a point p,the length of the tangent to a circle is 8cm and distance of p from the centre of the circle is 17cm.find the radius of the circle.

Answer 1

   Let O be the centre of the circle PT be the tangent an OT be the radius and OP be the distance of p from the centre of the circle
From a point p Length of the tangent = 8 cm
Distance of p from centre of the circle =17 cm
OT² =  OP² - PT² = 17²-8² = 289 - 64 = 225
⇒ OT = √225 = 15 cm
Radius = 15 cm

Answer 2

The radius of the circle is 15cm.

Step-by-step explanation:

Given,

Length of the tangent = 8cm

Distance of the point P from the circle's center = 17cm

To find,

Radius of the circle = ?

Let O be the center of the circle,

so that OP = 17cm

Tangent is PA with length = 8cm

OA ⊥ PA, as radius is always ⊥ to the tangent,

∵ According to Pythagoras theorem,

OP^2 = OA^2 + PA^2

17^2 = OA^2 + 8^2

OA^2 = 289 - 64

OA = $\sqrt{225}$

OA = 15cm

Thus, the radius of the circle = 15 cm

Learn more: find the radius of the circle

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