An arc subtends a central angle measuring

Mathematics

1 answer:

barxatty [35]3 years ago

6 0

Answer:

The arc is one-third of the circumference.

Step-by-step explanation:

The area of a circumference = 2πr

C = 2πr ... (1)

If an arc subtends a central angle measuring 2π/3 rad,

The length of the arc = rθ

Given θ = 2π/3

Length of the arc L = r(2π)/3

L = 2πr/3... (2)

L = 1/3(2πr)

Since C = 2πr

L = 1/3C

This shows that the arc is one-third of the circumference.

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