VTMO 2021 — Grade 8 — vtmo Question 17

$ABC , M$ on $AB , BN$ parallel $CM$ meets extended $AC$ at $N , E$ midpoint $MN , K = AE \cap BC$. Find $\frac{KC}{KB}$ for $a ) M$ midpoint $AB$; $b ) AM = \frac{AB}{\sqrt{2}}$.