Multiple choice

If PT is a tangent at T to a circle whose centre is O and $OP = 41 cm, OT = 9 cm$, then tength of PT is

  1. $40 cm$
  2. $32 cm$
  3. $21 cm$

  4. None
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A Correct answer
Explanation

The radius OT is perpendicular to the tangent PT, so OPT is a right triangle. Therefore, PT = sqrt(OP^2 - OT^2) = sqrt(41^2 - 9^2) = 40 cm.

AI explanation

The radius OT is perpendicular to the tangent PT at the point of contact, creating a right-angled triangle POT. By the Pythagorean theorem, the length of PT squared equals OP squared minus OT squared, which is 41 squared minus 9 squared. Calculating 1681 minus 81 gives 1600, and the square root of 1600 is 40 cm.

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