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M2
Here the red line is rotated through 90˚.
Which point is the centre of rotation?
It looks as though the image goes through K and C and A [but we really need to prove it - the animation is just a demo].
If this is true, ie if the image is a diagonal of the other two squares, then we can say:
angle BAP = angle CKP = 45˚
and so the red line bisects the angle at A.