Triplication #2

Geometry Level 4

Let \(ABC\) be a non-obtuse triangle such that \(\overline{AB}\) \(>\) \(\overline{AC}\) and \(\widehat{B}\) \(=\) \(45^{\circ}\). Let \(O\) and \(I\) denote the circumcenter and incenter of triangle \(ABC\), respectively. Suppose that \(\sqrt{2}\cdot \overline{OI}= \overline{AB}-\overline{AC}\). If the product of all the possible values of \(\sin{A}\) can be written as \[\sqrt{\frac{1}{\sqrt{F}}-\frac{1}{G}},\] where \(F,G\) are all integers. Find \(\large \frac{G}{F}\).

×

Problem Loading...

Note Loading...

Set Loading...