xcX3v84RxoQ-4GxG32940ukFUIEgYdPy In reply to the first question, let $P$ be a scalene triangle $ABC$. Bisect its sides at $D$, $E$, $F$, and complete triangle $DEF$. Then by _VI, 2_ of Euclid's _Elements_ , $FE$, $ED$, $DF$ are parallel to $BC$, $AB$, $CA$, respectively, and therefore triangle $DEF$, which we may call $P'$, is similar to $P$.It can be seen that$$P=4P'$$Whether $P'$ is the smallest (or largest