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?
Answer & explanation
Correct answer: option 1
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 : \(\sqrt[]{2}\)