Problem H
Find the Point
Input: standard input
Output: standard output
Time
Limit: 2 seconds
In the picture
below you can see a triangle ABC. A point O is inside the
triangle ABC. Given the angles AOB, BOC and COA and
the coordinates of point A (x1,y1), B(x2,y2) and C(x3,y3)
your task is to find the coordinate of point O.
The input file
contains less than 1001 sets of input. The description of each set of
input is given below:
Each set of input is
expanded in two lines. First line contains six integers x1, y1,
x2, y2, x3, y3 (-200 <= x1,
y1, x2, y2, x3, y3 <=200).
The meanings of these integers are given in the problem statement and picture above.
The second line contains three integers, which denotes the values of angles AOB,
BOC and COA respectively in degree.
There will be no
such input where A, B and C are collinear. Point A,
B and C are always different. Input is terminated by a set where A,
B, C are all at the origin. Of course this case should not be
processed. In this problem if two values differ by less than 1e-8 then
they are equal.
For each set of
input you should produce two lines of output. First line contains the serial of
output as shown in the output for sample input. The next line should contain
two floating-point numbers Ox and Oy, which
denotes the abscissa and ordinate of point O respectively. These
floating-point numbers should have six digits after the decimal point. If there
is no such point O strictly inside the triangle print a line “IMPOSSIBLE”
instead. Errors less than 2e-6 will be ignored.
10 10 20 20 5 8 100 200 200 0 0 10 0 5 5 120 120 120 0 0 0 0 0 0 100 100 160 |
Case 1: IMPOSSIBLE Case 2: 5.000000 2.886751 |