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Perpendicular from the Center to a Chord Bisects the Chord

Two chords AB...

Question

Two chords AB and CD intersect at a point P within a circle.
If $A P = 4 c m, C P = 3 c m, P D = 8 c m,$ find $P B$ .

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Solution

When 2 chords intersect, the product of the segments of one chord is equal to the product of segment of the other.

$⟹ A P \times P B = C P \times P D$

$⟹ P B = \frac{3 \times 8}{4} = 6 c m$

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