Scaling a point from one 2d-space to another

Question

The input to my program is a (x, y) integer coordinate inside the blue region of this circle of radius 100. I want to scale the input coordinate from the blue area to the red area, maintaining the the x and y ratios.

(link to the Desmos plot: https://www.desmos.com/calculator/61f4y2r7r4)

I know how to do this with one dimension - this answer gives a good overview on performing linear scaling. I attempted to apply this approach to the x and y axes separately. Here is some example code that I wrote to model the image.

#include <math.h>
#include <stdio.h>

#define RADIUS 100

static int find_point_on_circumference(int val) {
    return sqrt(RADIUS * RADIUS - val * val);
}

static int scale(int val, int min_old, int max_old, int min_new, int max_new) {
    return (max_old == min_old)
             ? val
             : (((val - min_old) * (max_new - min_new)) / (max_old - min_old) + min_new);
}

int main() {
    int x = 15;
    int y = 96;
    int boundary_old_x = 10;
    int boundary_old_y = 10;
    int boundary_new_x = 30;
    int boundary_new_y = 20;

    int new_x = scale(
      x,
      boundary_old_x,
      find_point_on_circumference(y),
      boundary_new_x,
      find_point_on_circumference(y));

    int new_y = scale(
      y,
      boundary_old_y,
      find_point_on_circumference(x),
      boundary_new_y,
      find_point_on_circumference(x));

    if (sqrt(new_x * new_x + new_y * new_y) <= RADIUS) {
        printf("SUCCESS\n");
    } else {
        printf("FAIL\n");
    }

    return 0;
}

For this particular input, (15, 96), the result is outside of the circle. I can see that the reason for that is that my max-x bound is less than my min-x bound. I'm just not sure how I should be applying this scaling correctly in the first place.