Question : In a circle, two chords $AB$ and $CD$ intersect each other internally at point $P$. If $AB=16\; cm, PB =6\;cm $, and $PD =12\; cm$, then the value of $PC$ (in $cm $) is equal to:
Option 1: 3
Option 2: 8
Option 3: 6
Option 4: 5
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Correct Answer: 5
Solution : $AB =$ 16 cm $PB =$ 6 cm $\therefore AP =$ 16 – 6 = 10 cm $PD =$ 12 cm $PC = x $ cm $\because$ Two chords $AB$ and $CD$ intersect at point $P$ in a circle then, $AP \times PB = CP\times PD$. ⇒ $10\times 6 = x\times 12$ ⇒ $x = 5 \;cm$ Hence, the correct answer is 5.
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