Let f,g and h be the lengths of the perpendiculars from the circumcentre of ΔABC on the sides a,b, and c respectively, and af+bg+ch=1λabcfgh, then λ is :
A
4
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B
5
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C
6
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D
3
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Solution
The correct option is A4 Distance of circumcentre from to side BC is RcosA=f.
Similarly, g=RcosB,h=RcosC ⇒af+bg+ch=2(tanA+tanB+tanC)⇒af+bg+ch=2(tanAtanBtanC)=2abc8fgh ⇒af+bg+ch=14abcfgh∴λ=4