Answer C and D please!

#1. Concurrent Lines in a Triangle. Plot the points A=(6,0), B = (2,3), C = (0,0) in the xy-plane, forming the triangle ABC. (a) Find the midpoints D, E, F of the three sides of AABC, and find equations for the lines containing the medians AD, BE, CF. Next, find the point where these lines intersect, giving the coordinates for the centroid, G. Verify G trisects AD, showing AG = 2*GD. (b) Now use the perpendicular bisectors of the three sides of AABC in order to locate 0, the circumcenter. Find the circumradius R and given an equation of the circumcircle, verifying that the coordinates of A, B, C all satisfy this equation. (c) You can use perpendicular slopes, m =-1/m, to find equations for the altitudes of AABC, and then find the coordinates of the orthocenter, H. Once you have done that, verify that the centroid lies on the Euler line, which is determined by OH. (d) Give the center of the nine-point circle for AABC, give the value of its radius, and find an equation for the nine-point circle. List the nine points on this circle, checking that their coordinates satisfy the equation. (e) For bonus points, you can use the internal angular bisector theorem to find the points on the sides of AABC which lie on the angular bisectors. Then you can use the equations for the lines from the vertices to these points in order to find the incenter and inradius. #1. Concurrent Lines in a Triangle. Plot the points A=(6,0), B = (2,3), C = (0,0) in the xy-plane, forming the triangle ABC. (a) Find the midpoints D, E, F of the three sides of AABC, and find equations for the lines containing the medians AD, BE, CF. Next, find the point where these lines intersect, giving the coordinates for the centroid, G. Verify G trisects AD, showing AG = 2*GD. (b) Now use the perpendicular bisectors of the three sides of AABC in order to locate 0, the circumcenter. Find the circumradius R and given an equation of the circumcircle, verifying that the coordinates of A, B, C all satisfy this equation. (c) You can use perpendicular slopes, m =-1/m, to find equations for the altitudes of AABC, and then find the coordinates of the orthocenter, H. Once you have done that, verify that the centroid lies on the Euler line, which is determined by OH. (d) Give the center of the nine-point circle for AABC, give the value of its radius, and find an equation for the nine-point circle. List the nine points on this circle, checking that their coordinates satisfy the equation. (e) For bonus points, you can use the internal angular bisector theorem to find the points on the sides of AABC which lie on the angular bisectors. Then you can use the equations for the lines from the vertices to these points in order to find the incenter and inradius