acute angled triangle

We may use vector method as follows:

http://i388.photobucket.com/albums/oo325/loyitak1990/Feb09/Crazygeom1.jpg

2009-02-12 22:18:29 補充：
Since M is the mid-point of BC, the position vector of M relative to A is the half of the sum of the position vector of B pls position vector of C, both relative to A.

2009-02-12 22:18:33 補充：
Point of div. formula.
For a point P dividing a line segment RS in the ratio a:b, the position vector of P (relative to any point) can be expressed as:
p = (as + br)/(a + b)
where r and s are also the corresponding position vectors.

2009-02-13 14:33:29 補充：
Yes, you should notice that a and b are vectorial quantities which include the concept of direction. Therefore don't just simply use lengths as measurement.