Instruction

1

The median can be found using the theorem of Stewart. According to which, the square of the median is equal to a quarter of the amount of the matching squares of the sides minus the square of the side, which held the median.

mc^2 = (2a^2 + 2b^2 - c^2)/4,

where

a, b, c are sides

mc is the median to side C;

mc^2 = (2a^2 + 2b^2 - c^2)/4,

where

a, b, c are sides

**of a triangle**.mc is the median to side C;

2

The task of finding the median can be solved using additional constructions

2*(a^2 + b^2) = d1^2 + d2^2,

where

d1, d2 - diagonal of the resulting parallelogram;

from here:

d1 = 0.5*v(2*(a^2 + b^2) - d2^2)

**of the triangle**to the parallelogram and the solution using the theorem of the diagonals of a parallelogram.Extend the sides**of a triangle**and**the median**, to complete them to the parallelogram. Thus, median**of a triangle**is equal to half the diagonal of the resulting parallelogram, two sides**of the triangle**- its sides (a, b), and the third side**of the triangle**, which was a median, is the second diagonal of the resulting parallelogram. According to the theorem, the sum of the squares of the diagonals of a parallelogram is twice the sum of the squares of its sides.2*(a^2 + b^2) = d1^2 + d2^2,

where

d1, d2 - diagonal of the resulting parallelogram;

from here:

d1 = 0.5*v(2*(a^2 + b^2) - d2^2)