Sirko and Liutyi#1456
In a Great Clearing, there were two Great Trees: a Great Oak and a Great Plane Tree. Two dogs were tied to the Great Oak: Sirko, with a chain of length meters, and Liutyi, with a chain of length meters. One day, Sirko became tired of sitting near Liutyi and moved as far as his chain would allow from the Great Oak. Liutyi, seeing this, did the same and stretched his own chain to its limit. Thus, they both sat with their chains fully stretched until they noticed they were at the ends of a Straight Path, where the Great Plane Tree was also located. They realized the distance from the Great Oak to the Great Plane Tree was equal to the distance from the Great Oak to the Straight Path. Additionally, Sirko noticed that he had to run times farther along the Straight Path to reach the Great Plane Tree than Liutyi did.
Every dog in the Great Clearing knows that the Great Trees are considered points, and the Straight Path is a segment of a straight line.
Help Sirko and Liutyi find the distance from the Great Oak to the Great Plane Tree.
Three real numbers , , (0 < x, y, z < 10^7).
Print the distance from the Great Oak to the Great Plane Tree with decimal places. If this distance cannot be determined, print the word IMPOSSIBLE.
Example 1