scuffed proof of butterfly theorem
KM=LM, show NM=OM
i have no idea why this works and other approaches don't
, show
Let be intersection of . First we have and cyclic (can be verified by angle chasing and . This implies , so we have
Next,
Subtract from and to get
If we have then that is also equal to
But we established which implies , which gives us .
Very Weird