When he draws the perpendicular bisector to one side he finds points that are equidistant to the edges of the side, i.e. to two vertices of the triangle.
When he draws the perpendicular bisector of other side, he finds the points that are equidistant to two vertices, one of which is common to one of the first two vertices.
Then, where both bisectors intercept each other is a point that is equidistant from the three vertices of the triangle, so it is the center of a circumference that touches the three vertices of the triangle.
Then he can circumscribe a circle about the triangle.
