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  They do say "Offer may be withdrawn at any time", so don't delay if you want to check it out.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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Mensa Daily Puzzlers

For over 15 years Mensa Page-A-Day calendars have provided several puzzles a year for my programming pleasure.  Coding "solvers" is most fun, but many programs also allow user solving, convenient for "fill in the blanks" type.  Below are Amazon  links to the two most recent years.

Mensa 365 Puzzlers  Calendar 2017

Mensa 365 Puzzlers Calendar 2018

(Hint: If you can wait, current year calendars are usually on sale in January.)


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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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