Hi all,

I'm a first time forum poster, so if I'm doing anything wrong then just let me know and I will fix it.

The question: The square PQRS has points A and B within its area such that PA, RB and AB are of equal length. Lines PA and RB are parallel. What is the lowest possible value for angle SPA?

My thoughts so far: So farm I've come up with two possible routes to a solution. The first involves creating some expressions for certain values within the question involving trig, and then creating and solving a trig inequality. The second involves creating a polynomial equation where y = angle SPA, and then performing optimisation to find the lowest value. The second option seems (to me at least) to be more promising. The only progress that I have made, however, is forming some basic trig expressions for a few lengths. I don't think that I have anything which is actually useful.

I'm looking for someone to point me in the right direction, and perhaps to help me start to solve this question, as I would like to figure most of it out for myself. Any help at all would be much appreciated.

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