In the given figure, OP and OQ are perpendicular bisectors of chords CD and AB respectively. If PD = 4 cm and OP = OQ = 3 cm, then calculate the length of chord AB.

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Solution

Since OP is the perpendicular bisector of chord CD, we have $C P = P D = 4 cm$
(Perpendicular drawn from the center to a chord bisects the chord)
$⟹ C D = C P + P D = (4 + 4) cm = 8 cm$

Also, given that $O P = O Q .$
We know that chords equidistant from center are equal in length.
Therefore, $C D = A B = 8 cm .$

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In the given figure, OP and OQ are perpendicular bisectors of chords CD and AB respectively. If PD = 4 cm and OP = OQ = 3 cm, then calculate the length of chord AB.

Since OP is the perpendicular bisector of chord CD, we have CP=PD=4 cm (Perpendicular drawn from the center to a chord bisects the chord) ⟹CD=CP+PD =(4+4) cm =8 cm Also, given that OP=OQ. We know that chords equidistant from center are equal in length. Therefore, CD=AB=8 cm.​​