CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Question 8
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?


Solution

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.

ˆAB=I=θ1360×2πr

ˆCD=I=θ2360×2π(2r)=θ2360×4πr

From Eqs. (i) and (ii)

θ1360×2πr=θ2360×4πr

θ1=2θ2

i.e angle formed by sector of C1 is double the angle formed by sector C2 at centre.

Therefore, the given statement is true.

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image