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Three overlapping triangles

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Draw three triangles, such that each overlaps a different vertex of the other two. That is, in triangles A,B,C with vertices (A1,A2,A3), (B1,B2,B3), (C1,C2,C3), you'll find B1 and C2 inside triangle A, C1 and A2 inside triangle B, and A1 and B2 inside triangle C.
Can this be done with isosceles right triangles?
What is the smallest internal angle possible in the triangles?
What is the smallest rectangle which holds all three triangles?

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post-53237-0-03488900-1372011166_thumb.j

These are the 3 angles that satisfy the OP as long as their side are intersecting.

3 right isosceles can do. Minimum angle is nil, i.e. keep all ends fixed,and move a vertex away..

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