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Texture on Disk in Mathematica 8?

Is it possible to apply a texture to a disk?

Applying a texture to a polygon works fine:
Graphics[{Texture[<<Texture Image>>], 
  Polygon[{{0, 0}, {1, 0}, {1/2, 1}}, 
   VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1/2, 1}}]}]

But when I try to apply it to a disk I get a solid, black circle:
  Graphics[{Texture[<<Texture Image>>], Disk[{0, 0}, 1]}]


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