/**
 * \author Andrew Mustun, CVH © 2024
 * \return Solutions for circles (<=4) that are tangential to the two given circles
 * and the given point.
 */
Apollonius.getSolutionsPCC = function(point, circle1, circle2) {
    if (!isPointShape(point) ||
        !isCircleShape(circle1) ||
        !isCircleShape(circle2)) {

        return [];    // Empty, no solutions
    }

    // Relative sized inversion circle (FS#2590): 
    var rInv = circle1.getRadius();
    if (circle2.radius > circle1.radius) {
        rInv = circle2.getRadius();
    }
    var inversionCircle = new RCircle(point.getPosition(), rInv);

    // Construct inversion shapes:
    var c1Inverse = Apollonius.getInverseShape(circle1, inversionCircle);
    var c2Inverse = Apollonius.getInverseShape(circle2, inversionCircle);

    // Get all tangent shapes for given inversion shapes:
    // Exploits an enhanced algorithm by CVH
    var tangents = Apollonius.getAllTangents(c1Inverse, c2Inverse);

    // Return the re-inversion of all tangents (0-4 solutions):
    return Apollonius.getInverseShapes(tangents, inversionCircle);
};