Determine the intersection of a segment, having ad edge in the center of circle, with the circle itself

intersect.ts

/**
 * Determine the intersection of a segment, having ad edge in the center of circle,
 * with the circle itself
 */
function intersect(
  xc: number,
  yc: number,
  radius: number,
  x1: number,
  y1: number
): { x: number; y: number } | null {
  const distanceFromCenter = Math.sqrt((x1 - xc) ** 2 + (y1 - yc) ** 2);
  const isInside = distanceFromCenter < radius;

  if (isInside) return null;

  // Segment ends on the circumference
  if (distanceFromCenter === radius) return { x: x1, y: y1 };

  const slopeRad = Math.atan2(y1 - yc, x1 - xc);
  const x = xc + radius * Math.cos(slopeRad);
  const y = yc + radius * Math.sin(slopeRad);

  return { x, y };
}

const inside = intersect(0, 0, 3, 1, 1);
const circumferenceRight = intersect(0, 0, 3, 3, 0);
const circumferenceTop = intersect(0, 0, 3, 0, 3);
const circumferenceTopRight = intersect(
  0,
  0,
  3,
  2.121320343559643,
  2.121320343559643
);
const outsideTopRight = intersect(0, 0, 3, 4, 4);
const outsideX = intersect(0, 0, 3, 4, 0);
const outsideTopLeft = intersect(0, 0, 3, -4, 4);

console.log({
  inside,
  circumferenceRight,
  circumferenceTop,
  circumferenceTopRight,
  outsideTopRight,
  outsideX,
  outsideTopLeft
});