Multiple choice

The length of a tangent from a point $A$ at a distance $5cm$ from the centre of the circle is $4cm$. The radius of the circle is

  1. 4cm

  2. 5cm

  3. 3cm

  4. 9cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a circle, the radius, tangent, and the line from the center to the external point form a right-angled triangle. Radius^2 + Tangent^2 = Distance^2. r^2 + 4^2 = 5^2 -> r^2 + 16 = 25 -> r^2 = 9 -> r = 3.

AI explanation

The line drawn from the center of the circle to the external point A forms a right-angled triangle with the tangent and the radius. Here, the hypotenuse is the distance from the center to point A, which is 5 cm, and one leg is the tangent length of 4 cm. Using the Pythagorean theorem, the radius squared equals 5 squared minus 4 squared, giving 25 minus 16, which is 9. Taking the square root of 9, the radius of the circle is 3 cm.

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