Multiple choice

A tangent is drawn to a circle from a point $P$ which is at a distance of $13$ cm from the center of the circle of radius $5 cm.$ The length of the tangent is?

  1. $10cm$
  2. $12cm$
  3. $18cm$

  4. None of the options
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The radius, the tangent, and the line from the center to the external point form a right-angled triangle. By the Pythagorean theorem, the tangent length is sqrt(13^2 - 5^2) = sqrt(169 - 25) = sqrt(144) = 12 cm.

AI explanation

The radius connecting the center of the circle to the point of tangency is perpendicular to the tangent, creating a right triangle. Using the Pythagorean theorem, we calculate the length squared as 13 squared minus 5 squared. This equals 169 minus 25, giving a result of 144, so the length of the tangent is 12 cm.

Keep practicing — related questions