Calculating Fluke: Subtract A or R?

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The discussion focuses on the calculation of fluke in geometry, specifically addressing the differences in subtracting values in two scenarios. In the first case, the calculation involves subtracting the length of segment 'a' from 'r', while in the second case, 'r' is subtracted from '2a'. The distinction arises from the geometric configuration of the triangles involved, where similar triangles ABC and DEC are utilized to establish the relationships. The lengths of the segments are defined as 'r - 2a' and '2a - r' respectively, highlighting the importance of understanding the geometric context.

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Edwardy
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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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