Multiple choice

A line segment through a point p cuts a given circle in $2$ points $ A$ & $B$ , such that $PA=16$ & $PB=9$, find the length of tangent from point to the circle

  1. $7$
  2. $25$
  3. $12$
  4. $8$
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C Correct answer
Explanation

By the Tangent-Secant Theorem, the square of the tangent length equals the product of the external segment and the whole secant segment. Tangent^2 = PA * PB = 16 * 9 = 144. Tangent = 12.

AI explanation

According to the tangent-secant theorem, the square of the length of the tangent from an external point equals the product of the lengths of the two segments from that point to the circle. Given the lengths as PA equals 16 and PB equals 9, the square of the tangent length is 16 multiplied by 9, which is 144. Taking the square root of 144 gives the length of the tangent as 12.

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