How to use Pythagoras theorem solve geometric math problem?
For a better overview let us denote AB by c, AC by b, AM by m and BC by a. Let P denote the point where the line through A perpendicular to a meets a. Further denote AP by h. With this setup we have APB, APC and APM to be three triangles with a right angle at the vertex P. Denote BP by x, CP by y and MP by z. From all this we get (using Pythagoras) x^2+h^2 = c^2 and y^2+h^2 = b^2 and z^2+h^2 = m^2 From the construction of x, y and z it is furthermore clear that a = x+y and a/2 = x+z (the possibility that a/2 = y+z is logically ruled out since b>c and hence x
