calculatePerpendicularIntersect

function calculatePerpendicularIntersect(centerPosition, startPosition, endPosition) {
  const { x: cX, y: cY } = centerPosition;
  const { x: sX, y: sY } = startPosition;
  const { x: eX, y: eY } = endPosition;

  const slopeStart = (cX - sX) / (cY - sY);
  const slopePerp = 1 / slopeStart;

  const intersectX = (slopeStart * sX - slopePerp * eX + eY - sY) / (slopeStart - slopePerp);
  const intersectY = (intersectX - sX) * slopeStart + sY;

  return {
    x: intersectX,
    y: intersectY
  };
}

function calculateControlPoint(centerPosition, startPosition, endPosition, perc) {
  const perpIntersect = calculatePerpendicularIntersect(centerPosition, startPosition, endPosition);
  return {
    x: startPosition.x + (perpIntersect.x - startPosition.x) * perc,
    y: startPosition.y + (perpIntersect.y - startPosition.y) * perc
  }
}