Triangle from 3 lines

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As of October, 2016, Embarcadero is offering a free release of Delphi (Delphi 10.1 Berlin Starter Edition ).     There are a few restrictions, but it is a welcome step toward making more programmers aware of the joys of Delphi.  They do say "Offer may be withdrawn at any time", so don't delay if you want to check it out.  Please use the feedback link to let me know if the link stops working.


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Given three line segments, L1,L2,L3, construct a triangle if possible by defining the coordinates of the three corners.

Here's the math to determine the coordinates of the third point if the line labeled L1 (and with length L1) is placed horizontally starting at coordinates (0,0).

1. L22 = s2 + a2                                         (Pythagoras)
2. L32 = (L1-s)2 + a2                               (Pythagoras)
3. L22 - s2 = L32 -(L1- s)2                        (Identity - solve 1 & 2 for a2)
4. L22 - s2 = L32 - L12 + 2*L1*s - s2      (Expand 3.)
5. s = ( L22 + L12 - L32) / (2*L1)            (Solve 4. for "s")
6. a = sqrt( L22 - s2 )                                 (Solve 1. for "a")

The program lets you view the effect of changing side lengths by drawing the resulting triangle and displaying the (s, a) coordinate.

Running/Exploring the Program 

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