If-a-b-c-are-sides-of-triangle-show-that-1-b-c-a-a-1-c-a-b-b-1-a-b-c-c-lt-1- Tinku Tara June 4, 2023 Algebra 0 Comments FacebookTweetPin Question Number 13223 by Tinkutara last updated on 16/May/17 Ifa,b,caresidesoftriangleshowthat(1+b−ca)a(1+c−ab)b(1+a−bc)c<1 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 17/May/17 if:a=b=c⇒RHS=1≮LHS=11+b−ca=2×p−ca,1+c−ab=2p−ab,1+a−bc=2p−bc(RHS)1=(1+b−ca)(1+c−ab)(1+a−bc)⇒(RHS)1=8×(p−a)(p−b)(p−c)abc=8×S2p4RS==2SpR=2rR⩽1(accordingtoEuler′steorem)d2=R2−2Rr=R(R−2r)⩾0⇒R⩾2rabc=2SsinC.2RsinC=4R.S,S=p.r(1+b−ca)a(1+c−ab)b(1+a−bc)c<(1+b−ca)abc(1+c−ab)abc(1+a−bc)abc=[(1+b−ca)(1+c−ab)(1+a−bc)]abc==(2rR)abc⩽1abc⩽1. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Solve-the-equation-xy-5x-5y-25-i-yz-3y-5z-15-ii-xz-5z-3x-15-iii-Next Next post: if-x-3-y-3-3axy-find-dy-dx-in-terms-of-x-and-y-and-prove-that-dy-dx-cannot-be-equal-to-1-for-finite-values-of-x-and-y-except-x-y-please-help- Leave a Reply Cancel replyYour email address will not be published.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.