Marinada '23

[lang = hr] Neka su točke $E,F,G$ redom polovišta stranica $AB,BC,AD$ četverokuta $ABCD$. Poznato je da je $GE$ okomito na $AB$, $GF$ okomito na $AC$ te da je $\angle DGC=30^{\circ}$. Ako se pravci $AB$ i $CD$ sijeku u $P$, pravci $EF$ i $BD$ u $Q$, a pravci $PQ$ i $DE$ u $T$ odredi $\angle DTP$. Rješenje zaokruži na dvije decimale. [/lang] [lang = en] Let the points $E,F,G$ respectively be the halves of the sides $AB,BC,AD$ of the quadrilateral $ABCD$. It is known that $GE$ is perpendicular to $AB$, $GF$ is perpendicular to $AC$ and that $\angle DGC=30^{\circ}$. If lines $AB$ and $CD$ intersect in $P$, lines $EF$ and $BD$ in $Q$, and lines $PQ$ and $DE$ in $T$ determine $\angle DTP$. Round the solution to two decimal places. [/lang]