Question 21
$ABCD$ is a parallelogram and $AB \ne BC$. $M$ is chosen so that
(1) $\angle MAC = \angle DAC$ and $M$ is on the opposite side of $AC$ to $D$, and
(2) $\angle MBD = \angle CBD$ and $M$ is on the opposite side of $BD$ to $C$.
Find $AM/BM$ in terms of $k = AC / BD$.
(1) $\angle MAC = \angle DAC$ and $M$ is on the opposite side of $AC$ to $D$, and
(2) $\angle MBD = \angle CBD$ and $M$ is on the opposite side of $BD$ to $C$.
Find $AM/BM$ in terms of $k = AC / BD$.