If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r , 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 false? Why?
Let two circles C1 and C2 of radius r and 2r with centres O and O′ respectively.
It is given that, the arc length ˆAB of C1 is equal to arc of length ˆCD of C2 i.e. ˆAB=ˆCD=I (say).
Now let θ1 be the angle subtended by arc ˆAB and θ2 be the angle subtended by arc ˆCD at the centre.
From Eqs. (i) and (ii)
i.e angle formed by sector of C1 is double the angle formed by sector C2 at centre.
Therefore, the given statement is true.