Determine x-coordinate of 3rd point on CIRCLE from y-coordinate and 2 other points

Question

I'm trying to construct an arc for a custom engineering curve. Say that the arc is on a circle having points $A: (x_1, y_1)$, $B: (x_2, y_2)$, and $C: (x_3, y_3)$, where $x_1 < x_2 < x_3$ and $y_1 < y_2 < y_3$. Also, $y_1 = mx_1$, where $m$ is a constant. The center and radius are unknown. How do I solve for $x_1$? Thank you for any assistance.