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 Calculating a Circle by 3 Points Coordinates  Unknown 16.12.1992

Формулы и программа для вычисления радиуса и координат центра окружности, проходящей через три заданные точки.
The formulas and a program to calculate a circle radius and coordinates of centre point.



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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