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Ive tried finding the intersection point that I labeled I.

first try:

Because I know the points A and M1 I found |AM1|

Then I said |AM1| = |AI| + |IM1| and proceeded to solve and came up with

-16 = 2(I

Second attempt:

Law of Cosines

First I found the angle between AB and MC

Second: Used law of cosines

|MI|

This way was going to be just as complicated so I stopped.

How can I solve this problem without using the fact that |M1| = 1/3|MC| and |IC| = 2/3|MC| or c.m?

first try:

Because I know the points A and M1 I found |AM1|

Then I said |AM1| = |AI| + |IM1| and proceeded to solve and came up with

-16 = 2(I

_{1})^{2}+I_{2})^{2}+ I_{3})^{2}) - 10I_{1}- 8I_{2}- 3I_{3}+√(blah blah blah)Second attempt:

Law of Cosines

First I found the angle between AB and MC

Second: Used law of cosines

|MI|

^{2}= .......This way was going to be just as complicated so I stopped.

How can I solve this problem without using the fact that |M1| = 1/3|MC| and |IC| = 2/3|MC| or c.m?