AD , BE, CF are the perpendiculars from the angular points of a triangle ABC upon the opposite sides . the perimeter of the triangle DEF and triangle ABC are in the ratio -
1]2r/R
2]r/2R
3]r/R
4]r/3R

 

Dear Student,
Please find below the solution to the asked query:

We know that DEF is known as Pedal Triangle.Sides of traingle are acosA,bcosB,ccosCHencePerimter of DEFPerimter of ABC=acosA+bcosB+ccosCa+b+c=2RsinAcosA+2RsinBcosB+2RsinCcosC2RsinA+2RsinB+2RsinC=sin2A+sin2B+sin2C2sinA+sinB+sinCUsing conditional identities, we getsin2A+sin2B+sin2C2sinA+sinB+sinC=4sinA.sinB.sinC24cosA2.cosB2.cosC2=2sinA2.cosA2.2sinB2.cosB2.2sinC2.cosC2.2cosA2.cosB2.cosC2=4sinA2.sinB2.sinC2=rR Answer

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards

  • 8
sry
  • 1
What are you looking for?