find-the-greatest-possible-square-insribed-in-a-triangle-with-sides-a-b-c- Tinku Tara June 4, 2023 Geometry 0 Comments FacebookTweetPin Question Number 39458 by MJS last updated on 06/Jul/18 findthegreatestpossiblesquareinsribedinatrianglewithsidesabc Commented by MJS last updated on 06/Jul/18 thesidesofthesquarenotnecessarilyononeofthesidesofthetriangle Commented by ajfour last updated on 06/Jul/18 In△PCRs2sinγ=b−ysin(θ+π4)….(i)In△SRAssinα=ysin(β−θ)…..(ii)eliminatingyamongst(i),(ii)s2sin(θ+π4)sinγ=b−ssin(β−θ)sinα⇒\boldsymbols=\boldsymbolb2sin(\boldsymbolθ+\boldsymbolπ4)sin\boldsymbolγ+sin(\boldsymbolβ−\boldsymbolθ)sin\boldsymbolα=bsinθ+cosθsinγ+sinβcosθ−cosβsinθsinα=bsinγsinαsinθ(sinα−cosβsinγ)+cosθ(sinα+sinβsinγ)\boldsymbols=bsinγsinαAsin(θ+ϕ)\boldsymbolwheretan\boldsymbolϕ=sinα+sinβsinγsinα−cosβsinγ\boldsymbolA=(sinα−cosβsinγ)2+(sinα+sinβsinγ)2forstobemaximumsin(θ+ϕ)hastobeminimum.Formanyofthecases(thoughnotall),sin(θ+ϕ)isminimumifθ=0Then\boldsymbolsmax=\boldsymbolbsin\boldsymbolγsin\boldsymbolαAsin\boldsymbolϕ=bsinγsinαsinα+sinβsinγandsincesinαa=sinβb=sinγc=12R\boldsymbolsmax=abc2aR+bc=a2aRbc+1.Thisformulawillhavetobeamendedifsin(θ+ϕ)<sinϕfornonzeroθ. Commented by ajfour last updated on 06/Jul/18 Commented by MJS last updated on 06/Jul/18 thanks.Ialreadythoughttherewouldbeseveraldifferentcases… Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-39457Next Next post: c-cosxsiny-xy-dx-sinx-cosy-dy-faind-integral-on-the-opposite-sid-of-the-clock-face-in-the-c-unit-circle-solve-this- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.