stylistic:style_transfer, structural:scholar_edition
Second example

A triangle ABC has a fixed side with length c. Determine the locus of the third vertex C such thatthe medians from A and C are orthogonal.

Choose an orthonormal coordinate system such that A (− c /2, 0), B (c /2, 0). C (x, y) is the variable third vertex. The center of is M ((2 x + c)/4, y /2). The median from C has a slope y / x. The median AM has slope 2 y /(2 x + 3 c).

The locus of the vertex C is a circle with center (−3 c /4, 0) and radius 3 c /4.