Techniques for analyzing Comparator circuits?
I generally first make an assumption about the state of the comparator (is it sinking, or is it high impedance) then do the derivations.

First assume the comparator is sinking. Because it's sinking, assume that pin 2 is at \$V_{EE} \$ potential. You may also assume that the comparator is able to sink enough current through \$R_{PULL-UP}\$ as to not allow it to source any current onto the R1-R2 net. The voltage at pin 10 becomes a simple voltage divider.

Next assume the comparator is high-impedance. Now you have a net with three resistors and two voltage sources (\$V_{REF}\$ and \$V_{PULL-UP}\$), since the comparator is (ideally) out of the equation now. Find the total current in the branch and calculate the voltage.