Multiple choice

Find the length of the tangent to a circle with radius $5$ cm, from a point at a distance of $13$ cm from the center.

  1. $12$ cm
  2. $24$ cm
  3. $18 $ cm
  4. $35$ cm
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A Correct answer
Explanation

The radius, tangent, and distance from center form a right triangle with the distance from the center as the hypotenuse. Tangent length = sqrt(13^2 - 5^2) = sqrt(169 - 25) = sqrt(144) = 12 cm.

AI explanation

The tangent, the radius at the point of contact, and the line from the center to the external point form a right-angled triangle. Using the Pythagorean theorem, we calculate the tangent length as the square root of (13^2 - 5^2) cm. This gives the square root of (169 - 25), which is the square root of 144. The length of the tangent is 12 cm.

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