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Alessandra Tomasi, Created with GeoGebra
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Change the value of the ∠alpha and vary the length of the radius then observe:
What changes and what remains the same? What kind of relationship is between the arc and radius?
The constant relationship arc/raduis is the measure in of the ∠alpha.
Therefore if the circumference of unit radius is considered the measure of an angle in radians coincides with the length of the corresponding arc.