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 r=135.26 r2 a/2=2096.58   r2 (135.26/r)/2=2096.58  135.26r=4193.16  r=31.000739  a=135.26/r=135.26/31.00074.3631 rad  r=31.000731.0007=31.001  dm 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 =a 180π  =249.98846181458  =250=2495918"f = a \rightarrow \ ^\circ = a \cdot \ \dfrac{ 180 }{ \pi } \ \ ^\circ = 249.98846181458 \ \ ^\circ = 250 ^\circ = 249^\circ 59'18"



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