Multiple choice

A point P is 13 cm from the centre of a circle. The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle.

  1. 8 cm

  2. 4 cm

  3. 5 cm

  4. 7 cm

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The radius, tangent, and the line from the center to the point form a right triangle where the line from the center is the hypotenuse. 13^2 = 12^2 + r^2. 169 = 144 + r^2. r^2 = 25, so r = 5.

AI explanation

The tangent at any point on a circle is perpendicular to the radius at that point, so the radius, the tangent, and the line from the center form a right triangle. Using the Pythagorean theorem, the radius squared plus the tangent length squared equals the distance from the center squared. Substituting the values gives radius squared plus 12 squared equals 13 squared, so radius squared equals 169 minus 144, which is 25, making the radius 5 cm.

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