  We propose a technique called Rotate-and-Kill for solving the polygon
inclusion and circumscribing problems. By applying this technique, we obtain
$O(n)$ time algorithms for computing (1) the maximum area triangle in a given
$n$-sided convex polygon $P$, (2) the minimum area triangle enclosing $P$, (3)
the minimum area triangle enclosing $P$ touching edge-to-edge, i.e. the minimum
area triangle that is the intersection of three half-planes out of the $n$
half-planes defining $P$, and (4) the minimum perimeter triangle enclosing $P$
touching edge-to-edge.
  Our algorithm for computing the maximum area triangle is simpler than the
alternatives given in [Chandran and Mount, IJCGA'92] and [Kallus, arXiv'17].
Our algorithms for computing the minimum area or perimeter triangle enclosing
$P$ touching edge-to-edge improve the $O(n\log n)$ or $O(n\log^2n)$ time
algorithms given in [Boyce \emph{et al.}, STOC'82], [Aggarwal \emph{et al.},
Algorithmica'87], [Aggarwal and J. Park., FOCS'88], [Aggarwal \emph{et al.},
DCG'94], and [Schieber, SODA'95].
