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This isn't really a Sage question. The angle between the center of the circle C, point D (or E), and F is a right angle. Thus, the angle DCE is 180 - 50 = 130 degrees. Half of the chord DE is a side of a right triangle opposite an angle of 130 / 2 = 65 degrees. Using the formula for sin and doubling we get the chord length to be
sage: 2*(2*sin(65/360*2*pi))
4*sin(13/36*pi)
sage: _.n()
3.62523114814660
