21306번 - Three Triangles 출처다국어

Starting with a △ABC with vertices A, B, C and sides a, b, c opposite A, B, C, respectively:

Construct the altitudes ha, hb and hc to sides a, b, c respectively (red) and the perpendicular bisectors pa, pb and pc to sides a, b, c (green):

Let A’ = hc intersect pb, B’ = ha intersect pc and C’ = hb intersect pa yeilding a new △A’B’C’ similar to ABC as shown on the below.

Finally, let A’’ = reflection of A’ in side b, B’’ = reflection of B’ in side c and C’’ = reflection of C’ in side a to obtain yet another similar triangle:

Write a program which takes as input the coordinates of the vertices A, B and C and outputs the areas of the three triangles.

Input consists of a single line which contains three, space separated floating point values Bx, Cx, Cy in that order (-1.0 ≤ Bx, Cx, Cy ≤ 10.0). △ABC will have area at least 1.0. The coordinates system is chosen so that A = (0, 0) is the origin and B = (Bx, 0) lies on the X-axis. C = (Cx, Cy) is arbitrary.

The output consists of a single line that contains three space separated floating point values to 4 decimal places. Area(△ABC), Area(△A’B’C’) and Area(△A”B”C”) in that order.