I found the answer.
For anyone else who might be looking for this solution:
The coordinates of the point dividing the line segment P1P2 in the ratio a/b are:
range = $\displaystyle (sqrt[b*b*r_1*r_1+a*a*r_2*r_2+2*a*b*r_1*r_2*cos(theta_2-theta_1)]/[a+b]$
theta = $\displaystyle arctan([b*r_1*sin(theta_1)+a*r_2*sin(theta_2)]/[b*r_1*cos(theta_1)+a*r_2*cos(theta_2)])$
It looks intimidating, but it isn't. The hardest part is making sure you have the correct sign after calculating arctan(). If you are implementing it in Java, you can use:
Code:
tempTheta = Math.atan2(tempRange, tempAz);
if(tempTheta < 0) tempTheta += (2 * Math.PI);
Math.atan2(y, x) computes the phase theta by computing an arc tangent of y/x in the range of -pi to pi. In the case of being negative, just add 2*PI.
For more on Points and Lines in Polar Coordinates, look here: Math Forum: Ask Dr. Math FAQ: Polar Coordinates
Thanks anyway!