Marinada '22

[lang=hr] U trokutu $ABC$ s najvećom stranicom $CA$ vrijedi $AB=279$, $BC=482$. Neka je $P$ polovište stranice $CA$, $S$ točka na stranici $AC$ tako da je $BS$ simetrala $\angle ABC$. Neka je $Q$ točka na $BC$ takva da je $SQ \perp BC$. Neka je $I=SQ \cap BP$. Nađi $\frac{SI}{QI}$. Odgovor zaokruži na $4$ decimale. [/lang] [lang=en] In the triangle $ABC$ with the largest side $CA$, $AB=279$, $BC=482$ is valid. Let $P$ be the midpoint of side $CA$, $S$ be a point on side $AC$ such that $BS$ is the bisector of $\angle ABC$. Let $Q$ be a point on $BC$ such that $SQ \perp BC$. Let $I=SQ \cap BP$. Find $\frac{SI}{QI}$. Round the answer to 4 decimal places. [/lang]