Question

PQRS is an equilateral quadrilateral. O is any point in PQRS. PO=RO, Then prove that Q,O,S lie on a straight line

Answer 1

An equilateral quadrilateral is one whose sides are equal. Hence it can be a rectangle or more generally it is a Rhombus. So we consider PQRS as Rhombus, whose diagonals are PR and QS.
We know, that diagonals of a Rhombus bisect each other at right angles. Hence, PR is perpendicular to QS.
Now any point O which is equidistant from P and R (PO = RO) must lie on its perpendicular bisector. Hence O will lie on QS.
This implies that Q, O and S lie in a straight line which is perpendicular bisector of PR.