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