You are given three points a, b, c on a page. Find if it’s possible to rotate the page around the point by an angle, such that the new position of ‘a’ is same as the old position of ‘b’, and the new position of ‘b’ is same as the old position of ‘c’. If such angle exists print “Yes”, else “No”.

Examples:

Input : a1 = 0, a2 = 1, b1 = 1, b2 = 1, c1 = 1, c2 = 0 Output : Yes Explanation : Rotate the page by 90 degree. Input : a1 = 1, a2 = 1, b1 = 0, b2 = 0, c1 = 1000, c2 = 1000 Output : No

Rotation of page by some angle is only possible if the distance between points ‘a’ and ‘b’ is equal to distance between points ‘b’ and ‘c’. But if the points are on same line, there is no rotation at point ‘b’. The problem has no solution when ‘a’, ‘b’, ‘c’ are in the same line or** dis(a, b) != dis(b, c)**

// C++ program to find if its possible // to rotate page or not #include<bits/stdc++.h> using namespace std; // function to find if it's possible // to rotate page or not void possibleOrNot(long long a1, long long a2, long long b1, long long b2, long long c1, long long c2){ // Calulating distance b/w points long long dis1 = pow(b1 - a1, 2) + pow(b2 - a2, 2); long long dis2 = pow(c1 - b1, 2) + pow(c2 - b2, 2); // If distance is not equal if(dis1 != dis2) cout << "No"; // If the points are in same line else if (b1 == ((a1 + c1) / 2.0) && b2 == ((a2 + c2) / 2.0)) cout << "No"; else cout << "Yes"; } // Driver Code int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); // Points a, b, and c long long a1 = 1, a2 = 0, b1 = 2, b2 = 0, c1 = 3, c2 = 0; possibleOrNot(a1, a2, b1, b2, c1, c2); return 0; }

Output:

No

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