In the square ABCD, point M is chosen inside such that ∠MAC = ∠MCD = α (see pic).
Determine the measure of ∠ABM.
It is easy to see that angle AMC is 135 degrees. Therefore, point M lies on a circle with center at point B and radius BA.
Therefore angle ABM=90 deg-2alpha.
In the above geometrical structure, find the value of tan(alpha) if d(M,AD)=sqrt(2) d(M,AC), where d(M,AD) and d(M,AC) are the distances from the point M to AD, respectively to AC.
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