Mathematics - Properties of Triangle Question with Solution | TestHub
MathematicsProperties of TriangleOrthocentre, pedal triangle basedMedium2 minQB
MathematicsMediumsingle choice
In an acute-angled triangle ABC, let f,g,h be the perpendicular distances from circumcenter to the side lines of lengths a,b,c, respectively. If a/f+b/g+c/h=/(fgh), find .
Options:
Answer:
A
Solution:
In an acute triangle, f=R cos A, g=R cos B, h=R cos C, so a/f=2tan A etc. As A+B+C=, tan A+tan B+tan C=tan A tan B tan C. Thus 2 A=2Πtan A=(1/4)(a/f)(b/g)(c/h), hence =1/4.
Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Orthocentre, pedal triangle based
⏱ 2mℹ️ Source: QB
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