Let F, G, H Be The Lengths Of The Perpendiculars From The Circumcenter ...

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SolveGuidesJoin / LoginUse appLogin0You visited us 0 times! Enjoying our articles? Unlock Full Access!Standard XIIMathematicsQuestionLet f,g,h be the lengths of the perpendiculars from the circumcenter of the ΔABC on the BC, CA, and AB, respectively, if af+bg+ch=λabcfgh, then the value of "λ" is
  1. 14
  2. 12
  3. 1
  4. 2
A1B2C14D12Open in AppSolutionVerified by Toppr

We know that angle made at the circumcenter is double the angle of the remaining vertex.In ΔOBD;tanA=a2f⟹af=2tanASimilarly; tanB=b2g⟹bg=2tanBtanC=c2h⟹ch=2tanCNow;af+bc+ch=2tanA+2tanB+2tanC=2tanA.tanB.tanC. [ If A+B+C=180°,tanA+tanB+tanC=tanA.tanB.tanC]2×a2f×b2g×c2h=14abcfghHence;λ=1/4891859_297020_ans_c5e1698bb0574b5da7f6e567e56ebec6.JPG

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