Can 5 points form exactly 8 right triangles and 64 points form at least 2005?

[sachinism]

Prove that there exist

(a) 5 points in the plane so that among all the triangles with vertices among these points there are 8 right-angled ones;

(b) 64 points in the plane so that among all the triangles with vertices among these points there are at least 2005 right-angled ones.

 

[CRGreathouse]

Source: Junior Balkan MO 2005

 

[sachinism]

Source: Junior Balkan MO 2005

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