Pentagon ABCDE is inscribed in a circle centered at the origin. Define the lines ABC = Line through the centroid of AABC perpendicular to DE, (BCD = Line through the centroid of ABCD perpendicular to AE, CDE = Line through the centroid of ACDE perpendicular to AB, (DEA = Line through the centroid of ADEA perpendicular to BC, LEAD = Line through the centroid of AEAB perpendicular to CD. As we see, these are lines going through the centroid of a triangle formed by three consecutive vertices, perpendicular to the line segment formed by the other two instance, here's &And in the picture: y E 4 &ABC D Prove that LABC, (BCD, LCDE, IDEA and EAB are concurrent, and find the expression for the position vector of the point they all go through. Activa Go to P Hint(S): First, find a parametrization for ABC in terms of the position vectors OA, OB, OC, OD, and OE. Start by figuring out a direction vector for this line