Obtain the location of point E on side AB such that ACDE is a trapezium

Question

In the traingle ABC, AB = 4.5cm , Ac = 9cm & angle ABC=90; The point D is located on BC such that DA = DC ;

Using only a straight edge with a cm/mm scale and a compass, construct and accurate diagram

Obtain the location of point E on side AB such that ACDE is a trapezium .

Help using a sketch would be much appreciated.

Answer 1

Hint:

The tringle $ABC$ is half an equlateral triangle because $\frac{\overline{AB}}{\overline{AC}}=\frac{1}{2}=\cos (\angle CAB)$.

Look at the figure and you can easily solve the problem.