TRICENTR - Triangle From Centroid

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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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arn200: 2021-01-13 15:21:16

AC :) using double instead of float helped..

kesarling: 2020-06-02 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: 2020-04-21 16:48:45

how to calculate orthocentre

aman_5050: 2020-04-16 17:25:42

The area I am getting for second set of input is 123287

mayankdhyani: 2018-04-09 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?
reply me on my email " mayankdhyani456@gmail.com ".

Last edit: 2018-04-09 14:25:14
aadarsh45: 2018-04-04 15:57:25

Use double instead of float

akhilb913: 2017-02-27 08:40:02

Finally!!

aexpo: 2016-06-25 08:50:01

AC :)
Solutions are correct,perfectly fine and simple!

Last edit: 2016-06-25 08:50:53
chandanak: 2015-10-24 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
and 3.897 0.000 .

puntu: 2015-09-11 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.


Added by:Patryk Pomykalski
Date:2004-05-22
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET