Calculating Fluke: Subtract A or R?

[Edwardy]

I need to calculate fluke.
Why do I in the first picture, when calculating the height, subract a from r, while in the other one, I subract r from a?
What does that depend on?
*I didn't translate the text because it is long and would take me a lot of time to do, but I will do it if it's neceserry.

 

[TSny]

Why do I in the first picture, when calculating the height, subract a from r, while in the other one, I subract r from a?
What does that depend on?

In one case, ##\mathbf{2}a## is subtracted from ##r##. In the other case, ##r## is subtracted from ##\mathbf{2}a##.

The reason for the difference is that the geometry is different for the two cases. But, in each case you use similar triangles to set up the relations.

For the first case you have the figure

The triangles ABC and DEC are similar. Note that the length of red segment CF is ##r - 2a##.

For the second case you have the figure

The triangles ABC and DEC are similar. Note that the length of EC is ##2a - r##.