2022 SSMO Relay Round 1 Problems/Problem 2

Problem

Let $T=$ TNYWR. Now, let $\ell$ and $m$ have equations $y=(2+\sqrt{3})x+16$ and $y=\frac{x\sqrt{3}}{3}+20,$ respectively. Suppose that $A$ is a point on $\ell,$ such that the shortest distance from $A$ to $m$ is $T$ . Given that $O$ is a point on $m$ such that $\overline{AO}\perp m,$ and $P$ is a point on $\ell$ such that $PO\perp \ell$ , find $PO^2.$

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2022 SSMO Relay Round 1 Problems/Problem 2

Problem

Solution