Multiple choice

Radius of a circle is 6 cm. The distance of a point lying outside the circle from the centre is 10 cm. The length of tangent drawn from the outside point to the circle is

  1. 5 cm

  2. 6 cm

  3. 7 cm

  4. 8 cm
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D Correct answer
Explanation

The radius, the tangent, and the distance from the center form a right-angled triangle where the distance from the center is the hypotenuse. Using Pythagoras theorem: tangent^2 + 6^2 = 10^2, so tangent^2 = 100 - 36 = 64, giving a length of 8 cm.

AI explanation

The tangent is perpendicular to the radius at the point of contact, so the radius, tangent and the line joining the centre to the external point form a right triangle. Using the Pythagorean theorem, the length of the tangent is the square root of (10^2 - 6^2). Calculating this gives the square root of (100 - 36), which is the square root of 64. The length of the tangent is 8 cm.

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