In a square PQRS, diagonal PR and QS intersect at O. The angle bisector ∠QPR meets SQ and RQ at U and T respectively. Find the ratio of OU : RT?

1 : \(\sqrt {2}\)

Let PQ = 2

Since PQ = RQ hence U and T will be midpoins of OQ and RQ

∴ RT = 1

Now SQ = 2\(\sqrt {2}\), OU = \(\frac{OQ}{2}\)

OU = \(\frac{2\sqrt {2}}{4}\) = \(\frac{1}{\sqrt {2}}\)

OU : RT = \(\frac{1}{\sqrt {2}}\)  : 1

OU : RT = 1 : \(\sqrt[]{2}\)