I have 3 points and their coordinates $(A, B, C)$. Then I have new coordinates of points $A'$ and $B'$ How to calculate the coordinates of point $C'$ knowing that the distance from point A to point C and the angle between line AB and line AC is the same. It must work as a formula in any program or on a sheet of paper.
Available
Point $A$ (the $x$ and $y$ coordinate) Point $B$ (the $x$ and $y$ coordinate) Point $C$ (the $x$ and $y$ coordinate) Point $A'$ (the $x$ and $y$ coordinate) Point $B'$ (the $x$ and $y$ coordinate)
$|A−C|=|A′−C′|$ but $|A−B|$ don't equal $|A′−B′|$
Angle between $AC$ and $AB$ is the same as $A'C'$ and $A'B'$
Unknown
All Angles
Point $C'$ (the $x$ and $y$ coordinate)
My conclusions
$AB=\sqrt{(Bx−Ax)^2+(By−Ay)^2}$
$AC=\sqrt{(Cx−Ax)^2+(Cy−Ay)^2}$
$CB=\sqrt{(Bx−Cx)^2+(By−Cy)^2}$
$A'B'=\sqrt{(B'x−A'x)^2+(B'y−A'y)^2}$