We will have the following:
First, we calculate AE as follows:
[tex]AE=\sqrt[]{AM^2-EM^2}[/tex]
Now, we replace values and solve it:
[tex]AE=\sqrt[]{16^2-11^2}\Rightarrow AE=3\sqrt[]{15}[/tex]
From theorem AE = EC therefore EC = esqrt(15); so, the following is true:
[tex]AC=AE+EC\Rightarrow AC=2AE\Rightarrow AC=2(3\sqrt[]{15})\Rightarrow AC=6\sqrt[]{15}[/tex]
Knowing this, we then determine FA as follows:
[tex]FA=\sqrt[]{AC^2-CF^2}[/tex]
We then determine BE, DM & CM as follows:
