Quarter circular

The wire that is hooked around the perimeter of quarter-circular arc has length 3π+12. Determine the radius of circle arc.

Result

r =  6

Solution:

$3 \pi+12= 2\pi r /4 + 2r \ \\ r = \dfrac{ 2\cdot (3 \pi +12) }{ \pi +4 } = 2 \cdot 3 \dfrac{ \pi +4 }{ \pi +4 } = 6$

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