I am attempting to calculate the intersection of two circle on the Earth with a given latitude, longitude and radius. I started with this [post](http://gis.stackexchange.com/questions/48937/how-to-calculate-the-intersection-of-2-circles). These circle will never be more than 100 km in diameter and will normally be "close" to each other, meaning two intersecting points for the pair of circles. I added a comment in the code below at the place where I am having the issue. Any help would be appreciated. NOTE: I originally asked this question on StackOverflow, but with this being so geospatial, I did not get any answers. var circle1 = {lat:37.673442, lon:-90.234036, r:107.5}; var circle2 = {lat:36.109997, lon:-90.953669, r:145}; function findInterscetionOfTwoCircles(circle1, circle2){ var c1 = latLonToGeocentricCoords(circle1); var c2 = latLonToGeocentricCoords(circle2); var r1 = convertRadians(circle1.r); var r2 = convertRadians(circle2.r); var c1dotc2 = calculateDotProduct(c1, c2); // This is where the problem is occurring. // The value of 'a' should be 0.9735030 but I am getting 46.770178816522844. // I am certain that r1 and r2 are correct (match the values in the original post). Additionally, I believe the calculateDotProduct function to be // correct, therefore making c1dotc2 correct. I think I have ruled out // any Order of Operations error. Maybe it is a degree/radian conversion // issue or something like it? I tried different variations and I and now out // of ideas. var a = (Math.cos(r1) - (Math.cos(r2) * c1dotc2)) / (1 - (c1dotc2 * c1dotc2)); var b = (Math.cos(r2) - (Math.cos(r1) * c1dotc2)) / (1 - (c1dotc2 * c1dotc2)); // -45.83805010474024, should be 0.0260194 var n = calculateCrossProduct(c1, c2); var x0 = calculateLinearCombination(a, b, c1, c2); var ndotn = calculateDotProduct(n, n); // var t = Math.sqrt((1 - calculateDotProduct(x0,x0))/calculateDotProduct(n,n)); // Finish the algorithm } function latLonToGeocentricCoords(circle){ var x = Math.cos(degToRad(circle.lon)) * Math.cos(degToRad(circle.lat)); var y = Math.sin(degToRad(circle.lon)) * Math.cos(degToRad(circle.lat)); var z = Math.sin(degToRad(circle.lat)); return {x:x, y:y, z:z}; } function geocentricCoordsToLatLon(x, y, z){ var lon = Math.atan2(x,y) var lat = Math.atan2(Math.sqrt((x*x)+(y*y)), z) return { lat: lat, lon: lon}; } function convertRadians(radius){ // converts NM right now return degToRad(radius) / 6; } function calculateDotProduct(input1, input2){ if(arguments.length !== 2){ throw new Error('You must supply two arguments to this method.'); } if(Array.isArray(input1) !== Array.isArray(input2) || typeof input1 !== typeof input2){ throw new Error('Inputs must be the same types.'); } var dotProduct = 0; if(Array.isArray(input1)){ // process as parallel arrays if(input1.length === input2.length){ throw new Error('Input lengths must be the same.'); } for(var i = 0, len = input1.length; i < len; i++){ dotProduct += input1[i] * input2[i]; } } else if(typeof input1 === 'object' && !Array.isArray(input1)){ // process as key-value object for(var key in input1){ if (input1.hasOwnProperty(key)) { if(!input2[key]){ throw new Error('Both inputs must have the same properties to be processed.'); } dotProduct += input1[key] * input2[key]; } } } return dotProduct; } function calculateCrossProduct(circle1, circle2){ var x = (circle1.y * circle2.z) - (circle1.z * circle2.y); var y = (circle1.z * circle2.x) - (circle1.x * circle2.z); var z = (circle1.x * circle2.y) - (circle1.y * circle2.x); return {x: x, y: y, z: z}; } function calculateLinearCombination(a, b, c1, c2){ var x = {x: a * c1.x, y: a * c1.y, z: a * c1.z}; var y = {x: b * c2.x, y: b * c2.y, z: b * c2.z}; return calculateDotProduct(x, y); } function degToRad(degree){ return degree * Math.PI / 180; } function radToDeg(radian){ return radian / Math.PI * 180; }