“费马点”是指位于三角形内且到三角形三个顶点距离之和最短的点。这个点与三角形三顶点连线构成的三个钝角都相等且为 120°。注意，这不是“费马大定理”。

package com.ai157.aigc.controller.test;
import javafx.application.Application;
import javafx.scene.Group;
import javafx.scene.Scene;
import javafx.scene.paint.Color;
import javafx.scene.shape.Circle;
import javafx.scene.shape.Line;
import javafx.stage.Stage;

public class FermatPoint extends Application {

    private static final int WIDTH = 600;
    private static final int HEIGHT = 400;

    @Override
    public void start(Stage primaryStage) {
        Group root = new Group();
        Scene scene = new Scene(root, WIDTH, HEIGHT);
     
        double x1 = 100, y1 = 100;
        double x2 = 400, y2 = 100;
        double x3 = 200, y3 = 300;

        Line line1 = new Line(x1, y1, x2, y2);
        Line line2 = new Line(x2, y2, x3, y3);
        Line line3 = new Line(x3, y3, x1, y1);
        line1.setStroke(Color.BLACK);
        line2.setStroke(Color.BLACK);
        line3.setStroke(Color.BLACK);
        root.getChildren().addAll(line1, line2, line3);

        double fermatX = (x1 + x2 + x3) / 3;
        double fermatY = (y1 + y2 + y3) / 3;
        Circle fermatPoint = new Circle(fermatX, fermatY, 5);
        fermatPoint.setFill(Color.RED);
        root.getChildren().add(fermatPoint);

        Line lineF1 = new Line(fermatX, fermatY, x1, y1);
        Line lineF2 = new Line(fermatX, fermatY, x2, y2);
        Line lineF3 = new Line(fermatX, fermatY, x3, y3);
        lineF1.setStroke(Color.BLUE);
        lineF2.setStroke(Color.BLUE);
        lineF3.setStroke(Color.BLUE);
        root.getChildren().addAll(lineF1, lineF2, lineF3);

        primaryStage.setTitle("Fermat Point Visualization");
        primaryStage.setScene(scene);
        primaryStage.show();
    }

    public static void main(String[] args) {
        launch(args);
    }
}

以上fermatX和fermatY是错误的，有人帮解？如何解题，得到x和y的坐标？