in the figure, O , P and R are the centers of three circles, each with radius 2 . what is the perimeter of the shaded region.
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Answer:
Assume a △OPR
in which OP=PR=OR=r=2
Hence, we can see that △OPR is Equilateral (with each angle = 60
o
)
also, the length of arc(OP)=
360
o
60
o
∗(2π∗2)=
3
2π
=18.84
Similarly, we can see that arc(OR),arc(RP) subtend equal angles(=60
o
)
So,arc(OP)=arc(OR)=arc(PR)=18.84
Hence, Perimeter of shaded Region =3∗18.84=56.52
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