Point inside circle
Circle with radius r (r is an integer) has point P inside it. Center of circle is M(r,r).
Points A,B,C are on the circumference: PA, PB and PC are different integers.
AngleAPB = angleBPC = angleCPA = 120 degrees (of course!).
I'm looking for hints/suggestions as to simplest way to "find" such circles,
and get coordinates of point P. Anybody got "short cuts"? Thanks.
Are you sure we can find such circle ?
Let be the length of respectively .
and be the sides respectively .
Then we have
If they are set to be integers , it is not a problem . However , the radius of the circumcircle is :
which is irrational .
EDIT : Oh , are not necessarily integers , my mistake , sorry .
Originally Posted by simplependulum
An example of such a circle: radius = 1729
x=715, y=1690, z=2288 ; a=3458, b=2717, c=2139.0827....
NOTE: BC (which is a) = diameter, but that's ok!