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Language: Euclid
Description In one of his notebooks, Euclid gave a complex procedure for solving the following problem. With computers, perhaps there is an easier way.
In a 2D plane, consider a line segment AB, another point C which is not collinear with AB, and a triangle DEF. The goal is to find points G and H such that: H is on the ray AC (it may be closer to A than C or further away, but angle CAB is the same as angle HAB) ABGH is a parallelogram (AB is parallel to HG, AH is parallel to BG) The area of parallelogram ABGH is the same as the area of triangle DEF ![]() Input There will be several test cases. Each test case will consist of twelve real numbers, with no more than 3 decimal places each, on a single line. Those numbers will represent, in order:
where point A is (AX,AY), point B is (BX,BY), and so on. Points A, B and C are guaranteed to NOT be collinear. Likewise, D, E and F are also guaranteed to be non-collinear. Every number is guaranteed to be in the range from -1000.0 to 1000.0 inclusive. End of the input will be signified by a line with twelve 0.0's. Output For each test case, print a single line with four decimal numbers. These represent points G and H, like this:
where point G is (GX,GY) and point H is (HX,HY). Print all values rounded to 3 decimal places of precision (NOT truncated). Print a single space between numbers. Do not print any blank lines between answers. Sample Input 0 0 5 0 0 5 3 2 7 2 0 4 1.3 2.6 12.1 4.5 8.1 13.7 2.2 0.1 9.8 6.6 1.9 6.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Sample Output 5.000 0.800 0.000 0.800 13.756 7.204 2.956 5.304 Source |
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