Question

A straight line is drawn curring two equal circles and passing through M the midpoint of the line joining the centres O and O'. Chord AB is equal to chord CD

• A. True
• B. False

Answer 1

The correct option is A

True

Draw OP $\perp$ AB and O'Q $\perp$ CD

In $△$ MOP and $△$ MO'Q

$\angle$ OMP = $\angle$ O'MQ (vertically opposite angles)

$\angle$ OPM = $\angle$ O'QM = ${90}^o$

OM = O'M (given)

Hence the two triangles are congruent by AAS criteria

$\Rightarrow$ OP = O'Q (cpct)

Chords that are equidistant from the centre are equal in length - Hence AB = CD