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Theorem 4:Equal Chords Are at Equal Distance from the Center

Two chords ...

Question

Two chords $A B$ and $C D$ of a circle intersect each other (externally) at $P$ outside the circle. If $A P = 10$ cm, $C P = 6$ cm and $P D = 5$ cm, find $P B$

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Solution

Here the chords $A B$ and $C D$ intersect each other at $P$ outside the circle.

$P A \times P B = P C \times P D$

$10 \times P B = 6 \times 5$

$P B = \frac{30}{10} = 3$ cm

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