Multiple choice

The radius of a circle is 5 cm. The distance of a point lying outside the circle from the centre is 13 cm. The length of the tangent drawn from the outside point to the circle is?

  1. 7 cm

  2. 9 cm

  3. 10 cm

  4. 12 cm

  5. 15 cm
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D Correct answer
Explanation

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

AI explanation

Using the right triangle property of a tangent, the radius to the point of tangency is perpendicular to the tangent line. This forms a right triangle with the outside point, the center, and the tangent point, allowing us to use the Pythagorean theorem. The length of the tangent is the square root of (13 squared minus 5 squared), which is the square root of (169 minus 25). The square root of 144 is 12 cm.

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