(Drag points) Draw a circle with three random points on the circle. Connect the points to...

(Drag points) Draw a circle with three random points on the circle. Connect the points to form a triangle. Display the angles in the triangle. Use the mouse to drag a point along the perimeter of the circle. As you drag it, the triangle and angles are redisplayed dynamically, as shown in Figure 1b. For computing angles in a triangle, see Listing 1.

FIGURE 1 (a) Exercise enables the user to drag vertices and display the angles dynamically. (b) Exercise enables the user to drag vertices along the circle and display the angles in the triangle dynamically.

LISTING 1 ComputeAngles.java

1 import java.util.Scanner;
2
3 public class ComputeAngles {
4 public static void main(String[] args) {
5 Scanner input = new Scanner(System.in);
6
7 // Prompt the user to enter three points
8 System.out.print("Enter three points: ");
9 double x1 = input.nextDouble();
10 double y1 = input.nextDouble();
11 double x2 = input.nextDouble();
12 double y2 = input.nextDouble();
13 double x3 = input.nextDouble();
14 double y3 = input.nextDouble();
15
16 // Compute three sides
17 double a = Math.sqrt((x2 - x3) * (x2 - x3)
18 + (y2 - y3) * (y2 - y3));
19 double b = Math.sqrt((x1 - x3) * (x1 - x3)
20 + (y1 - y3) * (y1 - y3));
21 double c = Math.sqrt((x1 - x2) * (x1 - x2)
22 + (y1 - y2) * (y1 - y2));
23
24 // Compute three angles
25 double A = Math.toDegrees(Math.acos((a * a - b * b - c * c)
26 / (-2 * b * c)));
27 double B = Math.toDegrees(Math.acos((b * b - a * a - c * c)
28 / (-2 * a * c)));
29 double C = Math.toDegrees(Math.acos((c * c - b * b - a * a)
30 / (-2 * a * b)));
31
32 // Display results
33 System.out.println("The three angles are " +
34 Math.round(A * 100) / 100.0 + " " +
35 Math.round(B * 100) / 100.0 + " " +
36 Math.round(C * 100) / 100.0);
37 }
38 }