Question

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 what will be the length of chord AB?

• A. 4 cm
• B. 5 cm
• C. 8 cm
• D. 6 cm

Answer 1

The correct option is C 8 cm

Since OP is the perpendicular bisector of chord CD, we have $CP=PD=4\text{cm}$
(Perpendicular drawn from the center to a chord bisects the chord)
$⟹CD=CP+PD=(4+4)\text{cm}=8\text{cm}$

Also, given that $OP=OQ.$
We know that chords equidistant from center are equal in length.
Therefore, $CD=AB=8\text{cm}.$