I am studying for an exam in my Computational Geometry course and stumbled upon the following question:

Given a group $H$ of $n$ half planes, such that $n \ge 3$.
we mark $C=\bigcap_{h\in H} h$ , and we know $C$ is not empty.
Describe an algorithm for finding a point in $C$ closest to the axes - supply the run time.

I was thinking of using Linear Programming similar to the half planes intersection problem, but I don't know how I should pick my goal function.
Would love to get some help in solving this problem!

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