Points A and B lie in the same plane. How many isosceles right triangles in the plane have A and B as vertices?

A) Three
B) Four
C) Five
D) Six
E) Infinitely many

That side can be the hypotenuse of such a triangle on either side of it, and it can also be one leg of such a triangle in 4 orientations. Look:


The smaller, darker triangles are where segment AB is the hypotenuse. The larger  triangles are the four other orientations.

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