Multiple choice

P is in exterior of $ C (0,15)$. A tangent from P touches the circle at T.If $PT=8$,then OP$=$

  1. $17$
  2. $13$
  3. $23$
  4. $7$
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A Correct answer
Explanation

A tangent to a circle is perpendicular to the radius at the point of tangency. This forms a right triangle OTP with the hypotenuse OP. OP^2 = OT^2 + PT^2. OT is the radius = 15. PT = 8. OP^2 = 15^2 + 8^2 = 225 + 64 = 289. OP = 17.

AI explanation

For a circle C(0, 15), the radius is 15. The line from the exterior point P to the center O forms a right triangle with the tangent segment PT, so we use the Pythagorean theorem: OP^2 = OT^2 + PT^2. Substituting the known values gives OP^2 = 15^2 + 8^2 = 225 + 64 = 289. Taking the square root of 289 gives OP = 17.

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