How can I calculate the ratio of the line segments in the following geometric scene?

The following code can draw the corresponding geometric scene. By observing for many times, we can know that the length ratio of line CE and line DE is fixed. How can I find the length ratio of them?

FindGeometricConjectures[
  RandomInstance[
    GeometricScene[{"A", "B", "C", "D", "E"}, 
      {Triangle[{"A", "B", "C"}], 
       GeometricAssertion[{"C", "E", "D"}, "Collinear"], 
       GeometricAssertion[{"A", "D", "B"}, "Collinear"], 
       EuclideanDistance["A", "D"] == 2 EuclideanDistance["D", "B"], 
       Triangle[{"A", "E", "D"}], Triangle[{"B", "E", "D"}], 
       PlanarAngle[{"A", "E", "B"}] == 135 °}]]]