program Three_Point_Test;
{Please upload simular formulas to Mr. Machinist BBS
=(716)434-1448
12/16/92
This program does not give the proper answer or I may be feeding
it improper coordinates. I need someone to tell me, "Yes, this
is the proper formula" or, "No, there is a mistake here!" or,
"Here is the right way to get the answer". I would like to know
if there is any one who can tell me what book this came out of.
I copied this formula from a book about two years ago but all I
know is that it was on page 63. I can't remember the title of
the book. If you know where I can find this formula or have a
similar one... please let me know.
There are some conditions that I'm sure must be meet. 1st of
all, all 3 X and Y coordinates MUST BE ON A CIRCLE. It is
possible to have 3 points that can not be on a circle!
If ya find out anything...please leave me mail on this BBS or
EXEC -PC or CHANNEL1 or PIER1 in Buffalo, NY or call my BBS.
Here is the formula!
Circle passing through 3 given points
=====================================
Let ( X1, Y1 ) = M1, ( X2, Y2 ) = M2, ( X3, Y3 ) =M3
1) The slope of the straight line joining M1 and M2 is;
Y2 - Y1
-------
X2 - X1
2) The slope of the perpendicular to this line is;
X2 - X1
- -------
Y2 - Y1
3) The equation of the bisector of the segment M1,M2 is;
Y1 + Y2 X2 - X1 X1 + X2
Y = ------- - -------- ( X - ------- )
2 Y2 - Y1 2
4) Similarly, the equation of the bisector of the segment
M1,M3 is;
Y1 + Y2 X3 - X1 X1 + X3
Y = ------- - ------- ( X - ------- )
2 Y3 - Y1 2
5) These 2 equations can be written in the form;
Y = K2X + H2
Y = K3X + H3
X2 - X1 X3 - X1
where; K2 = - ------- K3 = - ------- and
Y2 - Y1
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