Multiple choice

A point $P$ is $10cm$ from the centre of a circle. The length of the tangent drawn from $P$ to the circle is $8cm$. The radius of the circle is equal to

  1. $4cm$
  2. $5cm$
  3. $6cm$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The radius, tangent, and the line from the center to the point P form a right-angled triangle. By the Pythagorean theorem, r^2 + 8^2 = 10^2, which simplifies to r^2 + 64 = 100, so r^2 = 36 and r = 6cm.

AI explanation

The radius is perpendicular to the tangent at the point of contact, forming a right triangle with the tangent and the line from the center to point P. Using the Pythagorean theorem, the radius is equal to the square root of (10^2 - 8^2). This calculates to the square root of (100 - 64), which is the square root of 36. The radius of the circle is 6 cm.

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