parabola and triangle area (hint1)

Arthur Lee
This page provides supplementary materials for a problem from another page:
D is a point on AB, vertically above C. The length of CD is shown. When you drag the point C, you can see that the triangle area divided by CD gives a constant. Do you expect this? Can you explain how this constant is related to any part of this figure? If the area of the triangle is proportional to CD, we can make CD as long as possible to get the maximum area. So, how can you get the longest CD?
Continue to explore this problem with more suggestion in another page: