Question 5
$a$)In convex $ABCD , I$ midpoint $AC , M$ on $AC , AM = \sqrt{2}$ AI. Parallels from $M$ to $BC , DC$ meet $AB , AD$ at $E , F$. Prove $S_{IEF} = \frac{S_{MDB}}{2}$. $b$)Acute $ABC$ has median $AM$, altitude $BE , K = AM \cap BE , AM = BE$. Prove $AC = \sqrt{3} BK$.