scuffed proof of butterfly theorem
KM=LM, show NM=OM
i have no idea why this works
, show
Let be intersection of . First we have and cyclic (can be verified by angle chasing NDM and NAM. This implies , so we have
Next,
subtract 1, we get
if we have then that is also equal to
but we established that was equal to which implies
freakin weird
is some sort of diagram dependency necessary here