Hi Experts of CF . Please watch this problem .
I have been trying to solve this Geometry problem from a few Weeks ago . But every time I failed . My approach to solve this problem is ---
As 3 points are in same distance that simply means The point we will found in the result that will be a Center of a Circle whose radius is The distance of those 3 points distinctly. Let 3 points are ( x1, y1, x2, y2, x3 , y3 ). SO , we can write,
(x1 - H)^2 + (y1 - K)^2 = (x2 - H)^2 + (y2 - K)^2
=> (x1^2 + y1^2 -x2^2 -y2^2) - 2H(x1-x2) - 2K(y1-y2) = 0
=> A - 2HX1 - 2KY1 = 0 ------ ( i )
(x2 - H)^2 + (y2 - K)^2 = (x3 - H)^2 + (y3 - K)^2
=> (x2^2 + y2^2 -x3^2 -y3^2) - 2H(x2-x3) - 2K(y2-y3) = 0
=> B - 2HX2 - 2KY2 = 0 ------- ( ii )
And then we can Solute this two equation in the following way :
So,
A - 2HX1 - ( (B - 2HX2) / Y2 ) * Y1 = 0 [ Putting the value of 2K from eqn ( ii ) ]
=> H = ( AY2 - BY1 ) / ( 2 * ( X1Y2 - X2Y1 ) ) ----- (iii)
And,
=> K = ( B - 2HX2 ) / 2Y2 ----- ( iv )
Now , if those points are previously Co-Linear then I will print " Impossible " . But If not then we will do the above's Calculation . If ( H, K ) are in the same distance from those 3 points ( x1, y1, x2, y2, x3 , y3 ) the Print ( H, K ) else print " Impossible ".
Is my approach correct ( My code give answers " Impossible " for all test. ) ? If not then why ? Give me some Idea that how can I solve it ?? Thanks in Advance .
Anyone Help Me Please ? I am waiting .
Can you please give me your code??? Your approach is absolutely correct. But I think problem must be probably in comparing double or float values. Another problem may be if one point is midpoint of other two then that point is answer
Here is my Code : http://ideone.com/p7Pxxo @aayushkapadia
Sorry for late reply Here is your mistake Line 28: H = H/(calc1); Here don't divide directly . Instead do like this. if(H!=0) H = H/(calc1); Please see in other places also. This is because sometimes it will get 0/0 form if H=0
Also another problem is use of long long int. I got accepted by use of it
I remember seeing this problem in a contest, and using equations just like you, and never getting the AC verdict. I would always get WA or RTE (because of some division by 0). Then I thought it would be better find the triangle's circumcenter. The circumcenter (the center of the circumcircle) will be equidistant to the 3 points and is very easy to find.