10.1. In the field, there are two trees: an aspen 20 meters tall, and a birch 30 meters tall. The distance between the trees is 50 meters. On the top of each tree, there is a crow. Find a place on the ground for the cheese so that the sum of the two distances the crows fly from their locations to the cheese is minimized. What is this sum (in meters)? Round the answer to the nearest hundredth if necessary.
Solution. Place the "stone" 30 meters underground symmetrically to the second crow. The required total distance for the two crows is the length of the two-segment broken line connecting the first crow and this "stone" with the cheese. The shortest distance is a straight line. This results in a point located 20 meters from the first tree. The length of this shortest path: $20 \sqrt{2}+30 \sqrt{2}=50 \sqrt{2} \approx 70.71(\mathrm{M})$.