Question

In the adjoining figure, C and D are the centres of two circles which intersect at points M and N. If AMB || CD, then AB is equal to:

Options

• 4CD

• CD

• 2CD

• 3CD

Answer 1

2CD

Explanation:

Place C at x = 0 and D at x = CD = d.

The intersection point M of the two circles lies on the perpendicular bisector of CD.

So, its x-coordinate is `d/2`.

The horizontal line AB through M (AB || CD) meets the left circle at `x = -d/2` and the right circle at `x = (3d)/2`.

So, `AB = (3d)/2 - (-d/2)`

= 2d

= 2·CD

Thus,  AB = 2CD.