Question

Two diameters intersect each other at right angles. prove that the quadrilateral formed by joining their endpoints is a square.

Answer 1

OK
if two diameter intercept at right angle then they should have a center as mid points.(1)

NOW
if the diagonal of a square intercept each other at right angle & are perpendicular to each other(2)

now the diagonal are perpendicular to each other.(3) and if we join the end points of diagonal then we will get square ...... from (1)&(2)&(3)