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rbonito
Why isn't the answer E?

L = 2*Pi*R*C/360 (C is the central angle)

R = 2 and we know it's an Equilateral triangle with angles of 60 each, thus would be 2*60.

= 2*Pi*2*120/360

=4Pi/3

Really struggling with this so would really appreciate any insight. Thanks!

Kindly refer the image below to know the Central Angle Theorem
You are considering angle B as 60 degree in triangle BCD whereas it is actually 30 degree.
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Central Angle.png
Central Angle.png [ 58.36 KiB | Viewed 5092 times ]

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How do we know that the angle is 60 degree? I don't understand
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How do we know that the angle is 60 degree? I don't understand

Put a point (let’s call it X) at the midpoint of the diagonal. Now extend a line from the to point C you should notice that the sides of the equilateral triangle will be 2-2-2 thus each angle in our newly formed triangle will be 60 degrees.

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sonkarnishant
How do we know that the angle is 60 degree? I don't understand

Hey sonkarnishant,

You can use the following two properties of a rectangle to determine how it is an equilateral triangle (60 degree each).

1. Diagonals of a rectangle are equal in length.
2. Diagonals of a rectangle bisect each other.
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