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Bevis

Randvinklar till samma cirkelbåge är lika stora

Randvinklar som spänner upp samma cirkelbåge är lika stora. Det spelar ingen roll var randvinkeln placeras - den kommer alltid vara lika stor.
Foljderavrandvinkelsatsen misc 1.svg

Bevis

 Randvinklar till samma cirkelbåge är lika stora

För varje cirkelbåge finns en medelpunktsvinkel. Enligt randvinkelsatsen är alla randvinklar till samma cirkelbåge hälften av medelpunktsvinkeln dvs. lika stora.

Q.E.D.

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