Circle arc

Circle segment has a circumference of 135.26 dm and 2096.58 dm² area. Calculate the radius of the circle and size of central angle.

Result

r =  31.001 dm
f =  250 °

Solution:

$a \cdot \ r = 135.26 \ \\ r^2 \cdot \ a/2 = 2096.58 \ \\ \ \\ \ \\ r^2 \cdot \ (135.26/r) / 2 = 2096.58 \ \\ \ \\ 135.26r = 4193.16 \ \\ \ \\ r = 31.000739 \ \\ \ \\ a = 135.26/r = 135.26/31.0007 \doteq 4.3631 \ rad \ \\ \ \\ r = 31.0007 \doteq 31.0007 = 31.001 \ \text { dm }$

$f = a \rightarrow \ ^\circ = a \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ = 249.988461815 \ \ ^\circ = 250 ^\circ = 249^\circ 59'18"$

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