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#Processing, 101 97 bytes

4 bytes thanks to Flambino.

float d;void draw(){background(255);stroke(#800080);d+=PI/1800;point(50+cos(d)*38,50+sin(d)*38);} 

This creates a default 100 by 100 pixel window with the required animation.

^{Disclaimer: that image is not a GIF. Don't stare at it for a minute.}