Question

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

• A. square
• B. trapezium
• C. kite
• D. rhombus

Answer 1

The correct option is A

square

We know that equal chords in a circle are equidistant from the centre.
$\therefore OM=ON$
Also, since AB and CD are perpendicular, we have OM and PN to be parallel.
$⟹OM=PN,ON=MP$
i.e., $ON=PN=MP=MO$
Moreover, all angles measure ${90}^{\circ }$.
Therefore, the figure MONP is a square as all sides are equal and all angles measure ${90}^{\circ }.$