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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Ruffneck: 2014-11-11 01:24:56

maths maths maths

Harunur Rashid: 2014-08-18 22:36:53

b=a*ga/gb;
c=a*ga/gc;
how is it possible.Explain please

mayank: 2013-12-31 18:35:09

purely formula based! nothing sepcial required! and @liz can you tell how do you plan to do this question without the measure of length side 'a' ? My mail id is mayank25080562@gmail.com

liz: 2013-11-10 10:20:35

Actually the length of side a is not necessary. One can solve the problem using only distances from the centroid to the sides.

Mike Rush: 2013-02-15 12:46:09

Who can help me?

Mike Rush: 2013-02-15 12:45:43

It's too hard

Lloyd_feb: 2012-10-28 08:16:57

can some one help me.
I am getting WA for this prob. But on simulating the test case given here my output shows the correct answer.
What could be the problem? Iam printing the o/p correctly

P Venkata sri harsha: 2012-09-22 04:18:13

can anyone give more test cases i am struck with WA

The Vagabond: 2012-07-24 00:02:14

this question tests only mathematical skill.....anybody can search for formulas relating area of triangle in terms of given parameter :( :(
However,Second part of the problem seem quite interesting.:)

Last edit: 2012-07-24 00:19:20
saket diwakar: 2012-07-06 10:26:38

@all, no the given output is correct..my AC solution gives the same...


Added by:Patryk Pomykalski
Date:2004-05-22
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
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