I have filled circle and I want to add vertex at center of it. After that I want to connect vertices from circle to the center vertex (this part I know how to do).
4 Answers
If you've already added the circle there are some other fast ways to do this:
Method 1:
Select the circle.
Extrude (E), then cancel the translate part of the extrusion with Esc.
Press ⎇ AltM > Center to merge the extruded vertices into a single central vertex.

Method 2:
Select the circle.
Fill (F) to make an n-gon.
Poke Faces (⎇ AltP) to triangulate the n-gon with a central vertex.

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Darn, I can't do screen capture gifs. Excellent answer! – J Sargent Jan 11 '15 at 01:43
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2@NoviceInDisguise Why not? LICEcap works just fine for me.. – gandalf3 Jan 11 '15 at 01:44
You can do this when you first add the circle. When you first add the mesh, go to the tools where you normally enter the vertex number, and select Fill Type > Triangle Fan.

This will make a mesh like this:

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If it is necessary to use an existing mesh, select all the vertices in the circle, and press Shift-S Cursor to Selected.

Then deselect all, then hold Ctrl and click anywhere in the viewport. This will add a vertex.

Now press Shift-S Selection to Cursor. This will place it where the 3D cursor is located, which is in the exact center of the circle.

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Select the entire cicle A, then hit E > S > 0. in that order.
This will scale all vertices to 0.
Ctrl > V > remove doubles. To make a master vertex at center, rather than all thirty-two occupying the same space.
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