Question

Two circles with centre O and O' intersect at two points A and B. A line PQ is drawn parallel to OO' through B intersecting the circles at P and Q. Prove that PQ = 2OO'.​

Answer 1

ANSWER

Construct OM⊥PQ and O′N⊥PQ

So we get

OM⊥AP

We know that the perpendicular from the centre of a circle bisects the chords

We know that

O′N⊥AQ

We know that the perpendicular frmo the centre of a circle bisects the chord

AN=QN

It can be written as

AQ=2AN...(2)

So we get

PQ=AP+PQ

By substituting the values

PQ=2(AM+AN)

We get

PQ=2MN

From the figure we know that MNO′O is a rectangle

PQ=2OO′

Therefore, it is proved that PQ=2OO′