Question

In the given figure, AB and CD are equal chords of a circle with centre O. If AB and CD intersect each other at right angle at point P and perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.

Answer 1

We know that equal chords in a circle are equidistant from the centre.
$\therefore OM=ON$

OM and ON are perpendiculars, and AB and CD intersect at right angle, so $\angle OMP$, $\angle MPN$, and $\angle PNO$ are right angles.

Sum of angles of a quadrilateral is equal to four right angles.
Hence, $\angle MON$ is also a right angle.

So, all the angles of quadrilateral MONP are right angles and adjacent sides are equal.

Therefore, MONP is a square.