Do you know pythagorean theorem? well, if you take a pythagorean triangle with a fixed hypotenuse, and a fixed origin point, and only draw the other point of the hypotenuse for every possible angle, you'll get a circle.
Taking that on account.. your problem is easily solved, remembering trigonometry and that fun word 'sohcahtoa'
h : hypotenuse, radio of your circle
c_x,c_y : center of the circle
a : angle of the circle
sin definition:
sin a = opposite / hypotenuse
we can think of the opposite as the difference in y from the center, so we have
sin a = y / h .. y = h * sin(a) , here i'm assumpting that the centre of the circle is 0.. i guess that isn't your case, so we just offset it
y = h * sin (a) + c_y
cos definition:
cos a = adjacent / hypotenuse = x / h
x = h * cos (a) + c_x
so, here is your answer
x = h * cos (a) + c_x
y = h * sin (a) + c_y
where
h : hypotenuse, radio of your circle
c_x,c_y : center of the circle
a : angle of the circle
x,y : your points