TRICENTR  Triangle From Centroid
Given the length of side a of a triangle and the distances from the centroid (the point of concurrence of the medians  red in the picture) to all sides: a, b and c, calculate this triangle's area and the distance (blue line) from the orthocenter (the point of concurrence of the heights  green in the picture) to the centroid.
Input
In the first line integer n  the number of test cases (equal to about 1000). The next n lines  4 floating point values: the length of side a, and distances from the centroid to sides a, b and c.
Output
n lines consisting of 2 floating point values with 3 digits after the decimal point: the area of the triangle and the distance from the orthocenter to centroid.
Example
Input: 2 3.0 0.8660254038 0.8660254038 0.8660254038 657.8256599140 151.6154399062 213.5392629932 139.4878846649 Output: 3.897 0.000 149604.790 150.275
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kesarling:
20200602 18:53:05
RE: "distances from the centroid to sides a, b and c" Does that mean the length of the line drawn from the centroid to the midpoint of the sides a, b and c, or does it mean the perpendicular distance of centroid from the 3 sides?


dmachine7:
20200421 16:48:45
how to calculate orthocentre 

aman_5050:
20200416 17:25:42
The area I am getting for second set of input is 123287 

mayankdhyani:
20180409 14:24:21
I am finding difficulty in solving problems , please anyone suggest me what i should do advance my c++ programming skill. Can anyone suggest me the methods of solving the problems form the websites like this?


aadarsh45:
20180404 15:57:25
Use double instead of float 

akhilb913:
20170227 08:40:02
Finally!! 

aexpo:
20160625 08:50:01
AC :)


chandanak:
20151024 15:20:53
The solutions of this problem are not right . The person who framed the problem seems to have rounded off values somewhere in the intermediary steps . My answers for the sample input are : 149604.781 150.274


puntu:
20150911 18:37:28
though i am getting the correct answer in my ide but i think the rounding off trchnique followed by them and my ide i different, so they r giving me W/A.


puntu:
20150911 18:36:21
apply that the distance from the centroid to the orthocentre is twice that of the distance from the centroid to the circumcentre. so challenge is to calculate the distance from the centroid to the circumcentre.

Added by:  Patryk Pomykalski 
Date:  20040522 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 