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Question

In the figure, P and Q are the points of intersection of two circles with centres O and O. If straight lines, APB and CQD are parallel to OO, then what is the ratio of OO and AB?


  1. 1:3

  2. 1:2

  3. 1:4

  4. 3:4


Solution

The correct option is B

1:2


Draw OMAP and ONPB.

Now, quadrilateral OONM is a rectangle, since, all of its angles are 90

OO=MN

We know that, perpendicular from the centre of the circle to the chord bisects the chord, therefore

AM=MP=12AP and

PN=NB=12BP

OO=MN=PM+PN
=AP2+BP2
=(AP+BP)2
=AB2

OO:AB=1:2

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