Multiple choice

A tangent to a circle of radius 3 cm from an external point P is of length 4 cm. Find the distance of P from the nearest point of the circumference.

  1. 2 cm

  2. 3 cm

  3. 4 cm

  4. 5 cm

  5. 6 cm
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A Correct answer
Explanation

The distance from the center to the external point P is found using the Pythagorean theorem: sqrt(3^2 + 4^2) = 5 cm. The distance from P to the nearest point on the circumference is the distance from P to the center minus the radius, which is 5 - 3 = 2 cm.

AI explanation

The tangent is perpendicular to the radius at the point of contact, creating a right triangle with legs of 3 cm and 4 cm. Using the Pythagorean theorem, the distance from P to the center is sqrt(3^2 + 4^2) = sqrt(25) = 5 cm. The nearest point on the circumference lies along the line connecting P to the center, so the required distance is the hypotenuse minus the radius. This gives 5 - 3 = 2 cm.

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