diameter of a circle using 3 points on the circle

Hey everyone,

Does anyone know a formula or the fastest way (without drawing i hope) to calculate the diameter of a circle, when you have the coordinates of three points on that circle.

i need to do this for 15 measurements, so i'm not gonna draw every point, make a triangle and get the center so i can calculate the diameter from there.

this picture may clarify what i mean.

thanks in advance

 

ones you know the coordinates of the given points A,B, and C, you can find slopes of the lines passing through AB and BC
then you find equations of the lines perpendicular to segments AB and BC ; recall these lines will have a slope negative reciprocal to the slopes of lines passing through segments AB and BC

ones you get slopes, use the coordinates of one point and point slope formula to find equations of the lines perpendicular to segments AB and BC

then find their intersection point which will be the center of the circle

after you find coordinates of a center, use distance formula to find the length of radius, multiply by 2 and you will get diameter

 

Very cool.