P5: Let ABC be a scalene triangle with I as its incenter. Lines BI and AC intersect at P, and lines CI and AB intersect at Q. Suppose that IP=IQ, find∠A

this seems similar to problems we did on the Q section of this day where we needed to combine angle bisector theorem and law of sines to relate things to each other until we could find some angle, and we are given the additional condition that two segments are equal to each other. I have tried this way and haven't gotten to anything yet though.