I Calculating Fluke: Subtract A or R?

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Calculating fluke involves understanding the geometric relationships in different scenarios. The subtraction of a from r or vice versa depends on the specific configuration of the triangles involved. In one case, the length of the segment is determined by subtracting 2a from r, while in the other, r is subtracted from 2a. Both cases rely on the principle of similar triangles to establish the necessary relationships. The geometry of the situation dictates which subtraction method is appropriate.
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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.

Screenshot_20230413-094949.jpg

Screenshot_20230413-095006.jpg
 
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Edwardy said:
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
1681420826750.png

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
1681421093040.png

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