This is a follow-up to this blog, as a self-editorial for the three practice tasks from Medium-Hard to Hard. As solving the task after proving is quite easy (you can just directly use the techniques in the blog), I will only prove why the task is a convex optimization task.

#### JAG Summer Camp 2019 — "All your base are belong to us"

**Hint 1**

**Hint 2**

**Solution**

#### 2013 Japan Domestic Contest — "Anchored Balloon"

**Hint 1**

**Hint 2**

**Solution**

#### Asia Regional Contest 2007 in Tokyo — "Most Distant Point from the Sea"

**Hint 1**

**Hint 2**

**Solution**