The points L, M, N and O all lie on the same line segment, in that
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Check the picture below.
since the second figure is also a square, then the sides touching the diagonals have to be all equal, and that'd only happen if those sides bisects the larger square's diagonal.
since the second figure is also a square, then the sides touching the diagonals have to be all equal, and that'd only happen if those sides bisects the larger square's diagonal.