Marinada '23

[lang=hr] U trokutu $ABC$ s najvećom stranicom $CA$ vrijedi $AB=279$, $BC=482$. Neka je $M$ polovište stranice $CA$, $D$ točka na stranici $AC$ tako da je $BD$ simetrala $\angle ABC$. Neka je $E$ točka na $BC$ takva da je $DE \perp BC$. Neka je $F=DE \cap BM$. Nađi $\frac{DF}{EF}$. Odgovor zaokruži na $4$ decimale. [/lang] [lang=en] In the triangle $ABC$ with the largest side $CA$ it holds $AB=279$, $BC=482$. Let $M$ be the midpoint of side $CA$, $D$ be a point on side $AC$ such that $BD$ is the bisector of $\angle ABC$. Let $E$ be a point on $BC$ such that $DE \perp BC$. Let $F=DE \cap BM$. Find $\frac{DF}{EF}$. Round the answer to 4 decimal places. [/lang]