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1 초 128 MB 1 1 1 100.000%

문제

선영이의 조경회사는 컴퓨터 geek을 위한 정원 관리로 유명하다. 그 중 가장 유명한 것은 정삼각형 모양의 테라스에 원형 풀장이 내접하고 있는 형태이다.

그러나 선영이의 일부 고객은 정원 가운데 정삼각형 모양을 만드는 대신, 정원의 구석이나 비스듬한 면에 테라스를 만들기를 원한다. 선영이는 임의의 삼각형 모양에 대해 아래 그림과 같이 타원형의 풀장이 삼각형 변의 중점에 접하는 형태를 제안했다.

타원의 두 초점에 막대를 꽂으면, 막대에 줄을 연결해 타원을 그릴 수 있다. 삼각형의 세 꼭지점의 좌표가 주어졌을 때, 두 초점의 좌표와 필요한 줄의 길이를 출력하는 프로그램을 작성하라. (줄의 길이는 두 초점에서 타원 위의 임의의 점까지의 길이의 합이다.)

입력

입력의 첫 줄에는 테스트의 개수인 정수 N(1 ≤ N ≤ 1000)이 주어진다.

각각의 테스트에는 세 점의 좌표인 실수 x1, y1, x2, y2, x3, y3가 공백으로 구분되어 한 줄에 주어진다.

출력

각각의 테스트에 대해 한 줄에 fx1, fy1, fx2, fy2, rl(fx1<=fx2, fx1=fx2이면 fy1<=fy2)을 공백으로 구분하여 소수 둘째 자리까지 반올림하여 출력한다. (fx1, fy1)과 (fx2, fy2)는 각각 타원의 초점이며, rl은 줄의 길이이다. 타원이 원일 경우 두 초점은 같다.

예제 입력 1

3
100 100 200 273.2051 300 100
100 100 100 300 300 100
100 200 100 300 300 100

예제 출력 1

200.00 157.71 200.00 157.76 115.47
119.53 213.81 213.81 119.53 163.30
103.94 253.14 229.40 146.86 170.51
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(\uc904\uc758 \uae38\uc774\ub294 \ub450 \ucd08\uc810\uc5d0\uc11c \ud0c0\uc6d0 \uc704\uc758 \uc784\uc758\uc758 \uc810\uae4c\uc9c0\uc758 \uae38\uc774\uc758 \ud569\uc774\ub2e4.)<\/p>\r\n","input":"<p>\r\n\t\uc785\ub825\uc758 \uccab \uc904\uc5d0\ub294 \ud14c\uc2a4\ud2b8\uc758 \uac1c\uc218\uc778 \uc815\uc218 N(1 &le; N &le; 1000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8\uc5d0\ub294 \uc138 \uc810\uc758 \uc88c\ud45c\uc778 \uc2e4\uc218 x1, y1, x2, y2, x3, y3\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \ud55c \uc904\uc5d0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8\uc5d0 \ub300\ud574 \ud55c \uc904\uc5d0 fx1, fy1, fx2, fy2, rl(fx1&lt;=fx2, fx1=fx2\uc774\uba74 fy1&lt;=fy2)\uc744 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \uc18c\uc218 \ub458\uc9f8 \uc790\ub9ac\uae4c\uc9c0 \ubc18\uc62c\ub9bc\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4. (fx1, fy1)\uacfc (fx2, fy2)\ub294 \uac01\uac01 \ud0c0\uc6d0\uc758 \ucd08\uc810\uc774\uba70, rl\uc740 \uc904\uc758 \uae38\uc774\uc774\ub2e4. \ud0c0\uc6d0\uc774 \uc6d0\uc77c \uacbd\uc6b0 \ub450 \ucd08\uc810\uc740 \uac19\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2710","problem_lang":"1","title":"Joe\u2019s Triangular Gardens","description":"<p>Joe&rsquo;s landscaping company specializes in gardens for computer geeks who have just had their company go public. One of his signature features is a round pool surrounded by a tiled patio in the form of an equilateral triangle where the edge of the pool is tangent to each side of the triangle at its midpoint.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/tg.png\" style=\"height:193px; width:226px\" \/><\/p>\r\n\r\n<p>Unfortunately, some of Joe&rsquo;s customers are not satisfied with an equilateral triangle, usually in the center of the garden. Some want it in a corner or next to a slope or some other layout. Joe would like the option of offering arbitrary triangular patios with an elliptical pool which is tangent to each side at the center of the side. For example:<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/tgg.png\" style=\"height:234px; width:455px\" \/><\/p>\r\n\r\n<p>Joe knows how to draw an ellipse by putting two stakes in the ground (at the foci of the ellipse), tying a rope between them and dragging a marker stick inside the rope. What Joe would like is for the customer to determine where the corners of the triangle will be and then measure the location of the triangle vertices and compute where to put the stakes and how long to make the rope.<\/p>\r\n\r\n<p>Write a program, which takes as input the three vertices (x1, y1), (x2, y2) and (x3, y3) of a triangle and computes an ellipse inscribed in the triangle, which is tangent to each side of the triangle at its midpoint. The output is the coordinates of the two foci of the ellipse and the length of the rope (which is the sum of the distances from the foci to any point on the ellipse.<\/p>\r\n","input":"<p>The first line of input contains a single integer N, (1 &le; N &le; 1000) which is the number of data sets that follow. Each data set consists of a single line of input containing 6 space separated floating point numbers x1 y1 x2 y2 x3 y3 giving the coordinates of the vertices of a triangle.<\/p>\r\n","output":"<p>For each data set, you should generate one line of output with the following values: The data set number as a decimal integer (start counting at one), a space and five floating point values accurate to two decimal places each separated by a single space. The values are fx1 fy1 fx2 fy2 rl where (fx1, fy1) is one focus of the ellipse, (fx2, fy2) is the other focus of the ellipse and rl is the sum of the distances from the foci to any point on the ellipse (e.g. the length of the rope). The foci should be listed in increasing lexicographical order (i.e. fx1 &lt;= fx2 and if fx1 = fx2, fy1 &lt;= fy2). Note that in the case the ellipse is a circle, the two foci are the same (e.g. the center of the circle).<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]