Hello, tariqchpk!
There are two concentric circles with center O.
Given: Points $\displaystyle A, B, C, O, M$
. . . . .$\displaystyle OC = OA = OB = r,\;OC’ = OA’ = OB’ = R$
. . . . .$\displaystyle M$ is the midpoint of $\displaystyle AB$ and $\displaystyle A’B’.$
. . . . .$\displaystyle \angle OMB = \angle OMA = 90^o$
Find points $\displaystyle A’, B’, C’$ in cartesian coordinates.
Place center $\displaystyle O$ at the origin.
The larger circle has equation:
. . $\displaystyle x^2 + y^2 \:=\:R^2 \quad\Rightarrow\quad x \:=\:\pm\sqrt{R^2 - y^2}$
Let $\displaystyle m = MO.$
The horizontal line has equation:.$\displaystyle y = m$
The line and the circle intersect at:
. . $\displaystyle A'\left(\sqrt{R^2-m^2},\:m\right)\,\text{ and }\,B'\left(\text{-}\sqrt{R^2-m^2},\:m\right) $
And we have:.$\displaystyle C'(0,\,\text{-}R)$