finding the radius of one circle given 3 points and circle's center
show that the points A=(2,5) B=(6,1) C=(-3,5) lie on circle with center ( -1,2)..what is the radius of this circle
sorry to bother u guys so much..but i truly need ur help
Centre of circle and radius given 3 points on the circumference
The co-ordinates you have supplied in your example offer a very simple solution because 2 of your points fall along the same axis, making the centre of the circle=mean value of the 2 points. However should you need to find the centre and radius given 3 points, non of which fall on the same axis the following equations will be all you need. Having spent quite some time trawling through the equations for this problem I have (with some excell assistance from a colleague) managed to put together a straight forward layout suitable for use in excel and most programable calculators.
GIVEN CO-ORDINATES OF 3 POINTS ANYWHERE ON THE CIRCUMFERENCE OF A CIRCLE (X1,Y1), (X2,Y2) AND (X3,Y3)
THE FOLLOWING EQUATIONS WILL DETERMINE THE CO-ORDINATES OF THE CENTRE (X,Y)
THE RADIUS CAN NOW BE DETERMINED QUITE SIMPLY AS FOLLOWS
THIS WILL OF COURSE WORK WITH (X2,Y2) AND (X3,Y3)
YOU MAY FIND IT EASIER TO SUBSTITUTE X & Y WITH E & N SO THAT THE VALUES CAN BE INPUT DIRECTLY INTO THE APPROPRIATE CELLS IN EXCEL WITHOUT HAVING TO SCROLL ACROSS THE PAGE.