630P - Area of a Star - CodeForces Solution


geometry *2100

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Python Code:

import math
n, r = map(int, input().split())
d = math.pi - (math.pi/n) - (math.pi/(2*n))
a = r*math.sin(math.pi/n)/math.sin(d)
print(n*a*r*math.sin(math.pi/(2*n)))

C++ Code:

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<string>
#include<algorithm>
int n;
double r;
int main(){
	scanf("%d%lf",&n,&r);
	double A,B,C,a,b,c,s=0;
	a=r;B=acos(-1)/(2*n);C=acos(-1)/n;
	A=acos(-1)-B-C;
	b=a*sin(B)/sin(A);
	s=0.5*a*b*sin(C);
	s=2*n*s;
	printf("%.12f",s);
}


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