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​=11.1109/11.1558≐0.996 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​=11.4301/11.4737≐0.9962 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​=11.7491/11.7916≐0.9964 q36​ = q = 0.9962 n=36

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