Multiple choice

A point $P$ is outside a circle at a distance of $13\;cm$ from its centre. A secant from $P$ cuts the circle in $Q$ and $R$ such that $QR=7\;cm$ and the segment $PQ$ of the secant, exterior to the circle is $9\;cm$. Therefore, the radius of circle is

  1. $3\;cm$
  2. $4\;cm$
  3. $5\;cm$
  4. $6\;cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the secant be PQR where PQ=9 and QR=7. The whole secant PR = 16. Power of point P = PQ * PR = 9 * 16 = 144. Also, Power = d^2 - r^2, where d=13. 144 = 13^2 - r^2 = 169 - r^2. r^2 = 169 - 144 = 25. r = 5.

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