Given a triangle ABC. We add the origin to the circle center of the triangle. Then we have that the orthocenter H is given by H = A + B + C.

a) Set N = 1/2H. Show that N is equally far from the midpoints of the three 2 the line segments AB, BC and CA.

b) The circle with the center in N that passes through the three midpoints of the line segments AB, BC and CA intersects the triangle at 3 other points (in addition to the midpoints). Let D be one of these three points lying on BC. What do we know about the scalar product DA BC? Justify the answer.