Finding 3 rd point if 2 points and and 2 distances are given

Question

hi guys,
i got a problem while solving a geometry problem. problem description is as follows.
i have 2 points p1(x1, y1), p2(x2, y2), and i have to find the a point p3 which is d1 distance from p1, and d2 distance form p2.
here i have to get 2 points for point p3(x3, y3) because i dont know which direction it is.
how to solve this can anybody help me please.
regards,
vemula kiran kumar.
Message was edited by:
kirankumarvemula

Answer 1

hi,
i tried to solve as u said.
mean while i tried in some other manner. please can u tellme whether this is correct way or not.
please see my code.
* CirclesIntersectionPoints.java
* Created on March 15, 2007, 4:25 PM
* Vemula KiranKumar,
* Associate ID - 1997.
* GeoSpace Integrated Solutions,
* Hyderabad.
package com.org.Demarcation.importcoord;
* @author Vemula KiranKumar.
import java.lang.Math;
class CalculatePoints1 {
public static void main(String[] args)      {
CirclesIntersectionPoints newPoints = new CirclesIntersectionPoints(-9, 1, 7, 5, -5, 18);
System.out.println("In the main program-x1--->"+newPoints.getX1());
System.out.println("In the main program-y1--->"+newPoints.getY1());
System.out.println("In the main program-x2--->"+newPoints.getX2());
System.out.println("In the main program-y2--->"+newPoints.getY2());
*     This class is used to find the intersection points of two circles
*     Let Circle1 have a center point A(a,b), and Circle 2 have a center point B(p,q)
* and radious of circle 1 is r1, radious of circle 2 is r2,
* intersection points of circle 1 and circle 2 are E(X1, Y1) and (X2, Y2) that have to calculated by this program.
* procedure: -
* K = (1/4)squreroot(((r1+r2)^-d^)(d^-(r1-r2)^))
*     d^ = (x2-x1)^ + (y2-y1)^
* K is the area of the triangle formed by the centers of the two circles and one of their points of intersection;
* d is the distance between the circles centers;
*     r1, r2 are the circles' radii; (x1,y1) and (x2,y2) are the circles' centers
* The two solutions, then, are
* x = (1/2)(x2+x1) + (1/2)(x2-x1)(r1^-r2^)/d^ � 2(y2-y1)K/d^
* y = (1/2)(y2+y1) + (1/2)(y2-y1)(r1^-r2^)/d^ � -2(x2-x1)K/d^
class CirclesIntersectionPoints {
/* Default Constructor */
public CirclesIntersectionPoints(){
this.a=0;
this.b=0;
this.r1=0;
this.p=0;
this.q=0;
this.r2=0;
this.X1=0;
this.Y1=0;
this.X2=0;
this.Y2=0;
/* Parameterised constructor*/
public CirclesIntersectionPoints(double x1, double y1, double d1, double x2, double y2, double d2){
setA(x1);
setB(y1);
setR1(d1);
setP(x2);
setQ(y2);
setR2(d2);
System.out.println(this.a+", "+this.b+", "+this.r1+", "+this.p+", "+this.q+", "+this.r2 +" --> Real values ");
try {
interSectionPoints(); // finding the intersection points.
} catch (Exception ex) {
ex.printStackTrace();
} // finding the intersection points.
/*----------------Given Point 1(x1, y1) distance d1-------------*/
public double getA(){
return this.a;
private void setA(double x1){
this.a = x1;
public double getB(){
return this.b;
private void setB(double y1){
this.b = y1;
public double getR1(){
return this.r1;
private void setR1(double d1){
this.r1 = d1;
/*----------------Given Point 2(x2, y2) distance d2-------------*/
public double getP(){
return this.p;
private void setP(double x2){
this.p = x2;
public double getQ(){
return this.q;
private void setQ(double y2){
this.q = y2;
public double getR2(){
return this.r2;
private void setR2(double d2){
this.r2 = d2;
/*----------------New Point (X1, Y1) -------------*/
public double getX1(){
return this.p;
private void setX1(double newx1){
this.X1 = newx1;
public double getY1(){
return this.Y1;
private void setY1(double newy1){
this.Y1 = newy1;
/*----------------New Point (X2, Y2) -------------*/
public double getX2(){
return this.X2;
private void setX2(double newx2){
this.X2 = newx2;
public double getY2(){
return this.Y2;
private void setY2(double newy2){
this.Y2 = newy2;
/*----------------end of the getter setter ----------------------*/
* finding the Intersection points.
* x = (1/2)(x2+x1) + (1/2)(x2-x1)(r1^-r2^)/d^ � 2(y2-y1)K/d^
* y = (1/2)(y2+y1) + (1/2)(y2-y1)(r1^-r2^)/d^ � -2(x2-x1)K/d^
public void interSectionPoints() {
double aa = 0, bb = 0, rr1 = 0, pp = 0, qq = 0, rr2 = 0, sqrdistance = 0, areaoftri = 0;
double partx1 = 0, partx2 = 0, partx3 = 0;
double party1 = 0, party2 = 0, party3 = 0;
double x1 = 0, x2 = 0, y1 = 0, y2 = 0;
aa = getA();
bb = getB();
rr1 = getR1();
pp = getP();
qq = getQ();
rr2 = getR2();
sqrdistance = sqrdistBetweenCenters(); // getting the distance between the centers of circles.
areaoftri = areaofTriangle(); // getting the area of triangle.
* Now Calculate the partx1, partx2, partx3 for XX1, XX2 coordnates,
* and Calculate the party1, party2, party3 for YY1, YY2 coordnates.
* _x1 = partx1 + partx2 + partx3
* _x2 = partx1 + partx2 - partx3
* _y1 = party1 + party2 + party3        
* _y2 = party1 + party2 - party3        
sqrdistance = sqrdistBetweenCenters();
areaoftri = areaofTriangle();
* finding the X coordinates.
partx1 = (pp + aa) / 2;
partx2 = ((pp - aa) * ( (Math.pow(rr1,2) ) - (Math.pow(rr2,2)) ))/ (2 * sqrdistance);
partx3 = (2 * (qq - bb) * areaoftri) / sqrdistance;
_x1 = partx1 + partx2 + partx3;
_x2 = partx1 + partx2 - partx3;
* Setting the x coordinates
setX1(_x1);
setX2(_x2);
* finding the Y coordinates.
party1 = (qq + bb) / 2;
party2 = ((qq - bb) * ( (Math.pow(rr1,2) ) - (Math.pow(rr2,2)) ))/ (2 * sqrdistance);;
party3 = -(2 * (pp - aa) * areaoftri) / sqrdistance;
_y1 = party1 + party2 + party3;
_y2 = party1 + party2 - party3;
System.out.println("*******************");
System.out.println(_y1);
System.out.println(_y2);
setY1(_y1);
setY2(_y2);
* This method will calculate the K, area of the triangle ABE.
* K = (1/4)squreroot(((r1+r2)^-d^)(d^-(r1-r2)^))
* where d is the distance between the two centers.
* (a, b) --> center of circle 1, with radii r1(given distance d1)
* (p, q) --> center of circle 2, with radii r2(given distance d2)
public double areaofTriangle(){
double areaoftri = 0;
double part1 = 0;
double part2 = 0;
double sqrdistance = 0; //distance between
double aa,bb,rr1,pp,qq,rr2;
aa = getA();
bb = getB();
rr1 = getR1();
pp = getP();
qq = getQ();
rr2 = getR2();
System.out.println(aa+", "+bb+", "+rr1+", "+pp+", "+qq+", "+rr2+" -->OK Test Passed.");
* getting the square of distance between
* centers of 2 circles.
sqrdistance= sqrdistBetweenCenters();
System.out.println("squre distance is --->"+sqrdistance+" -->OK Test Passed.");
* calculating part1, part 2 and subsitute in formula
* K = (1/4)squreroot((part1)*(part2))
part1 = Math.pow((rr1 + rr2),2)- sqrdistance;
part2 = sqrdistance - Math.pow((rr1 - rr2),2);
areaoftri = (Math.sqrt(part1*part2))/4;
System.out.println("Area of Triangle is --->"+areaoftri+" ---> Not OK not Tested Yet");
return areaoftri;
* This method calculate the squre of distance between
* the two points of the circle centers
public double sqrdistBetweenCenters(){
double sqrdistance = 0;
double aa = 0, bb = 0, pp = 0, qq = 0;
aa = getA();
bb = getB();
pp = getP();
qq = getQ();
sqrdistance = (Math.pow((pp-aa),2)) + (Math.pow((qq-bb),2));
return sqrdistance; // OK. Test Passed.(kiran)
protected String kirankumarVemula;
/* Given Point 1(x1, y1) with distance d1*/
private double a;
private double b;
private double r1;
/* Given Point 2 (x2, y2) with distance d2*/
private double p;
private double q;
private double r2;
/* Calculated Point 1 */
private double X1;
private double Y1;
/* Calculated Point 2 */
private double X2;
private double Y2;
}