Question 185
be $ABCD$ a convex quadrilateral. be $P$ the intersection of $AC$ y $BD$. the angle $\angle APD = 60^\circ$. be $E, F, G$ y $H$ the midpoints of the sides $AB, BC, CD$ y $DA$ respectively. Find the largest positive real number $k$ such that
$$
EG + 3HF \geq k d + (1-k) s
$$
being $s$ The semiperimeter of the quadrilateral $ABCD$ y $d$ the sum of the lengths of their diagonals. When is equality achieved?
$$
EG + 3HF \geq k d + (1-k) s
$$
being $s$ The semiperimeter of the quadrilateral $ABCD$ y $d$ the sum of the lengths of their diagonals. When is equality achieved?