Multiple choice

Two equal chords $AB$ and $AC$ of the circle $x^{2}+y^{2}-6x-8y-24=0$ are drawn from the point $A(\sqrt{33}+3, 0)$. Another chord $PQ$ is drawn intersecting $AB$ and $AC$ at points $R$ and $S$, respectively given that $AR=SC=7$ and $RB=AS=3$. The value of $PR/QS$ is

  1. $1$
  2. $1.5$
  3. $2$
  4. $None\ of\ these$
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A Correct answer
Explanation

By the power of a point theorem for intersecting chords, AR * RB = PR * RS and AS * SC = QS * SR. Given AR=7, RB=3, AS=3, SC=7, we have 7*3 = PR * RS and 3*7 = QS * SR. Thus, PR * RS = QS * SR, which implies PR = QS, so PR/QS = 1.