I am attempting to calculate the intersection of two circle on the Earth with a given latitude, longitude and radius. I started with this http://gis.stackexchange.com/questions/48937/how-to-calculate-the-intersection-of-2-circles

These circles 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.

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 = convertRadius(circle1.r);
		var r2 = convertRadius(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 convertRadius(radius){
		// converts NM right now
		return degToRad(radius) / 60; 
	}
			
	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;
	}