Language: C++

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

struct Point {
	long double px, py;
};

struct Circle {
	long double px, py, r;
};

long double PI = 3.14159265358979;
long long N, K;
Point G[1 << 18]; long double C[1 << 18];
Circle H[1 << 18];

double dst(Point V1, Point V2) {
	return sqrt((V1.px - V2.px) * (V1.px - V2.px) + (V1.py - V2.py) * (V1.py - V2.py));
}

double dst(Circle V1, Circle V2) {
	return sqrt((V1.px - V2.px) * (V1.px - V2.px) + (V1.py - V2.py) * (V1.py - V2.py));
}

int solve(double T) {
	for (int i = 1; i <= N; i++) {
		H[i].px = G[i].px;
		H[i].py = G[i].py;
		H[i].r = T / C[i];
	}

	vector<Point> Major;
	for (int i = 1; i <= N; i++) {
		Major.push_back(Point{ H[i].px, H[i].py });
	}
	for (int i = 1; i <= N; i++) {
		for (int j = i + 1; j <= N; j++) {
			if (dst(H[i], H[j]) > H[i].r + H[j].r) continue;
			
			double DST = dst(H[i], H[j]);
			double DX = (H[j].px - H[i].px) / DST;
			double KAKUDO = acos(DX);
			if (H[j].py < H[i].py) KAKUDO = PI * 2.0 - KAKUDO;

			double cl = 0.0, cr = PI, cm;
			for (int k = 0; k < 50; k++) {
				cm = (cl + cr) / 2.0;
				double vx = H[i].px + H[i].r * cos(KAKUDO + cm);
				double vy = H[i].py + H[i].r * sin(KAKUDO + cm);
				double ds = dst(Circle{ vx, vy, 0.0 }, H[j]);
				if (ds < H[j].r) { cl = cm; }
				else { cr = cm; }
			}

			double tx = H[i].px + H[i].r * cos(KAKUDO + cm);
			double ty = H[i].py + H[i].r * sin(KAKUDO + cm);
			double ux = H[i].px + H[i].r * cos(KAKUDO - cm);
			double uy = H[i].py + H[i].r * sin(KAKUDO - cm);
			Major.push_back(Point{ tx, ty });
			Major.push_back(Point{ ux, uy });
		}
	}

	int maxn = 0;
	for (int i = 0; i < Major.size(); i++) {
		int cnt = 0;
		for (int j = 1; j <= N; j++) {
			double I = dst(G[j], Major[i]);
			if (I <= H[j].r + 1e-7) cnt++;
		}
		maxn = max(maxn, cnt);
	}
	return maxn;
}

int main() {
	cin >> N >> K;
	for (int i = 1; i <= N; i++) cin >> G[i].px >> G[i].py >> C[i];

	long double L = 0, R = 1e6, M;
	for (int i = 0; i < 50; i++) {
		M = (L + R) / 2.0;
		int I = solve(M);
		if (I >= K) { R = M; }
		else { L = M; }
	}
	printf("%.12Lf\n", M);
	return 0;
}

Compiler output:
a.cc: In function 'double dst(Point, Point)':
a.cc:20:16: error: 'sqrt' was not declared in this scope
   20 |         return sqrt((V1.px - V2.px) * (V1.px - V2.px) + (V1.py - V2.py) * (V1.py - V2.py));
      |                ^~~~
a.cc: In function 'double dst(Circle, Circle)':
a.cc:24:16: error: 'sqrt' was not declared in this scope
   24 |         return sqrt((V1.px - V2.px) * (V1.px - V2.px) + (V1.py - V2.py) * (V1.py - V2.py));
      |                ^~~~
a.cc: In function 'int solve(double)':
a.cc:44:41: error: 'acos' was not declared in this scope
   44 |                         double KAKUDO = acos(DX);
      |                                         ^~~~
a.cc:50:64: error: 'cos' was not declared in this scope
   50 |                                 double vx = H[i].px + H[i].r * cos(KAKUDO + cm);
      |                                                                ^~~
a.cc:51:64: error: 'sin' was not declared in this scope
   51 |                                 double vy = H[i].py + H[i].r * sin(KAKUDO + cm);
      |                                                                ^~~
a.cc:57:56: error: 'cos' was not declared in this scope
   57 |                         double tx = H[i].px + H[i].r * cos(KAKUDO + cm);
      |                                                        ^~~
a.cc:58:56: error: 'sin' was not declared in this scope
   58 |                         double ty = H[i].py + H[i].r * sin(KAKUDO + cm);
      |                                                        ^~~