Multiple choice

Find the length of the tangent drawn to a circle of radius $8cm$, from a point which is at a distance of $10cm$ from the centre of the circle.

  1. $3cm$
  2. $18cm$
  3. $12cm$
  4. $6cm$
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D Correct answer
Explanation

A tangent to a circle forms a right-angled triangle with the radius and the line from the center to the external point. Using the Pythagorean theorem, the square of the tangent length plus the square of the radius equals the square of the distance from the center: t^2 + 8^2 = 10^2. Thus, t^2 = 100 - 64 = 36, so t = 6cm.

AI explanation

The radius to the point of contact is perpendicular to the tangent line, forming a right triangle with the line segment from the center to the external point. Using the Pythagorean theorem, the tangent length squared equals the hypotenuse squared minus the radius squared, which is 10 squared minus 8 squared. This calculates to the square root of 36, giving a tangent length of 6 cm.

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