Multiple choice

A point is $17$ in. from the center of a circle of radius $8$ in. The length of the tangent from the point to the circle is

  1. $\sqrt{353}$
  2. $15$
  3. $9$
  4. $9\sqrt{3}$
  5. $15\sqrt{2}$
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B Correct answer
Explanation

The radius, tangent, and distance from center form a right triangle with the distance from center as the hypotenuse. Tangent length = sqrt(17^2 - 8^2) = sqrt(289 - 64) = sqrt(225) = 15.

AI explanation

The length of a tangent drawn from an external point to a circle is given by the formula L = sqrt(d^2 - r^2), where d is the distance from the point to the center and r is the radius. Substituting the given values, d = 17 and r = 8. We calculate L = sqrt(17^2 - 8^2) = sqrt(289 - 64). This simplifies to sqrt(225), which gives a tangent length of 15.

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