# Find coordinates for points on circle given R, 2 Points, and angle or 2 points and center?

I would like to find coordinates for points on a circle given:

1. Radius of circle
2. Coordinates of 2 points on the circle
3. Angle of point 1, center, and point 2.

Ultimately, I would like to write a formula in excel to calculate points on circle to stake out coordinates for surveying.

Thanks again for your help. Please let me know if I can provide any more information or rewrite question using better terminology.

-
This must be impossible to accomplish? – user143599 Apr 17 '14 at 17:59
Not quite. See below. – Mick Jul 4 '14 at 19:28

Refer to the diagram below:-

(1) From given A and B, draw the corresponding perpendicular bisector such that P is their point of intersection.

(1.1) The co-ordinates of P can be found (by midpoint formula).

(2) From the given angle (say, 2θ), bisect it such that it is θ + θ.

(3) Find y where y = R cos θ.

(4) From P, draw arcs with radius = R cos θ cutting the brown line at Q. (Note that there are two positions of Q.)

(5) Q is now the center and QA (or QB) is the radius of the circle required.

-