There are two non-intersecting convex polygon strictly inside a circle. The problem is to draw a line such that the polygons are on the different side of the line , the area of the part containing the first polygon is minimum. The inputs are such that you can always draw such a line. How to solve this problem ? number of points <= 50000

Problem name: circular island Problem link : https://codeforces.net/gym/101370/attachments/download/5499/20092010-summer-petrozavodsk-camp-petr-mitrichev-contest-5-en.pdf

How can I take preparation for attacking computational geometry problems appearing in world finals ? A good set of problems (if possible with solution) would very much help. Thank you

There is a problem from phuket regional 2015 that i have been trying to solve.

Here is the problem link : https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&category=690&page=show_problem&problem=5321

The problem transforms into something like this , there is a tree ( at most 10^5 nodes) where each node has two values(let them call a,b). Now there are some (at most 10^5) queries of form : U V x y .

You have to find all the nodes on path U to V for which a*x + b*y is minimum. Note that if this minimum occurs for several nodes , you have to find them all. It is guaranteed that you don't have to print more than 3*10^5 nodes' id.