If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2 r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement true or false? Why?

Question

Multiple choice

$ false,\quad since\quad the\quad radius\quad of\quad { C }_{ 1 }\neq the\quad radius\quad of{ \quad C }_{ 2 }.\quad \\ $
$ False,\quad \quad since\quad \theta _{ 1 }\neq \theta _{ 2 }.\\ $
$ True,\quad since\quad \theta _{ 1 }=\theta _{ 2 }.\\ $

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Accepted Answer

$ True,\quad since\quad the\quad radius\quad of\quad { C }_{ 1 }=2\times (the\quad radius\quad of{ \quad C }_{ 2 }).\quad \quad \\ $

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