Question Number 188260 by Humble last updated on 28/Feb/23
$$\boldsymbol{{ABCD}}\:{is}\:{a}\:{rectangle}\:{such}\:{that} \\ $$ $$\:\mid\boldsymbol{{AB}}\mid>\mid\boldsymbol{{BC}}\mid\:{and}\:{O}\:{is}\:{the}\:{mid}−{point} \\ $$ $$\:{of}\:\boldsymbol{{DC}},\:{if}\:\mid\boldsymbol{{OB}}\mid=\mathrm{0}.\mathrm{1}{m}\:{and}\:\angle\boldsymbol{{BOC}}\:=\boldsymbol{\theta}, \\ $$ $$\:{find}\:{an}\:{expression}\:{for}\:{the}\:{perimeter}\:{of} \\ $$ $$\:{the}\:{rectangle}\:{in}\:{terms}\:{of}\:\boldsymbol{\theta}.\:{Find}\:{also},\: \\ $$ $${the}\:{values}\:{of}\:\boldsymbol{{R}}\:{and}\:\boldsymbol{\beta}\:{for}\:{which}\:{the}\: \\ $$ $${perimeter}\:{is}\:\boldsymbol{{Rcos}}\left(\boldsymbol{\theta}−\boldsymbol{\beta}\right).\:{Deduce},\:{the}\: \\ $$ $${greatest}\:{possible}\:{value}\:{oc}\:{the}\:{perimeter}. \\ $$