Regular n-gon

Which regular polygon has a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm?

Correct answer:

n =  36

Step-by-step explanation:

R=10 cm r=9.962 cm q=r/R=9.962/10=0.9962 r35=1/tan(π/35)=1/tan(3.1416/35)11.1109 R35=1/sin(π/35)=1/sin(3.1416/35)11.1558 q35=r35/R35=11.1109/11.15580.996 r36=1/tan(π/36)=1/tan(3.1416/36)11.4301 R36=1/sin(π/36)=1/sin(3.1416/36)11.4737 q36=r36/R36=11.4301/11.47370.9962 r37=1/tan(π/37)=1/tan(3.1416/37)11.7491 R37=1/sin(π/37)=1/sin(3.1416/37)11.7916 q37=r37/R37=11.7491/11.79160.9964 q36 = q = 0.9962 n=36

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