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I would like to duplicate this graph:

I've used this code to draw the circle:

Graphics[{Circle[{0, 0}, 3, {-2Pi, 2Pi}]},PointSize[.025]]

But Mathematica complains about improperly formatted options, and I don't know how to proceed from here.

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Graphics[{{Green, Line[{{0, 0}, {1/Sqrt[2], 1/Sqrt[2]}}]}, {Red, 
  Line[{{1/Sqrt[2], 0}, {1/Sqrt[2], 1/Sqrt[2]}}]}, {Line[{{0, 1/Sqrt[2]},
    {1/Sqrt[2], 1/Sqrt[2]}}]}, {Green, PointSize[.03], 
  Point[{1/Sqrt[2], 1/Sqrt[2]}]}, {Circle[{0, 0}, 1, {-2 Pi, 2 Pi}]}}, 
  Axes -> True, Ticks -> {{0, 1/Sqrt[2]}, {0, 1/Sqrt[2]}}]

Mathematica graphics

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I added a picture & fixed formatting, I hope you don't mind :) – Öskå May 18 '14 at 16:00
    
@Öskå that is ok. thanks – Algohi May 19 '14 at 4:14

Such plane figures are amenable to using complex numbers instead of pairs of reals for their points, and hence readily drawn using David Park's Presentations add-on (http://home.comcast.net/~djmpark/DrawGraphicsPage.html):

Draw2D[{
   ComplexCircle[0, 1],
   Green, 
   ComplexLine[{0, (1 + I)/Sqrt[2]}], PointSize[0.025], ComplexPoint[(1 + I)/Sqrt[2]],
   Red, 
   ComplexLine[{1/Sqrt[2], (1 + I)/Sqrt[2]}], ComplexLine[{I/Sqrt[2], (1 + I)/Sqrt[2]}]
   },
   Axes -> True, Ticks -> {{1/Sqrt[2]}, {1/Sqrt[2]}}]

enter image description here

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