Multiple choice

From a point P, a tangent is drawn to a circle. If the length of the tangent is 3 cm and the distance of point P from the centre of the circle is 5 cm, find the radius of the circle.

  1. 3 cm

  2. 4 cm

  3. 5 cm

  4. 6 cm
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B Correct answer
Explanation

The tangent to a circle is perpendicular to the radius at the point of contact. This forms a right triangle with the radius (r), tangent (3 cm), and hypotenuse (5 cm). r^2 + 3^2 = 5^2, so r^2 = 25 - 9 = 16, r = 4 cm.

AI explanation

The radius is perpendicular to the tangent at the point of contact, forming a right-angled triangle with the line segment from the external point to the center. Using the Pythagorean theorem, we calculate the radius as the square root of (5 squared minus 3 squared), which is the square root of (25 minus 9). This gives the square root of 16, making the radius 4 cm.

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