As shown in the figure, in square ABCD, e and F are the midpoint of AD and DC respectively, BF and CE intersect at point M. verify that am is equal to ab

Link B, e
Easy certificate EC ⊥ BF
The four points a, B, m and E are in common circle
∴∠ABE=∠AME
∵∠AMB=90-∠AME
∠ABM=90-∠FBC
∠FBC=∠ABE=∠AME
∴∠ABM=∠AMB
∴AM=AB

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