If P1, P2, P3 are altitudes of a triangle ABC from the vertices A, B, C and is the area of the triangle, then...












1












$begingroup$


If P1, P2, P3 are altitudes of a triangle ABC from the vertices A, B, C and is the area of the triangle , then P^-1+P^-2+P^-3 is equal to






trigonometry







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  • 1




    $begingroup$
    We have $dfrac12P_1cdot a=triangle$ etc. So, $sumdfrac1{P_1 }=dfrac{sum a}{2triangle}=Rdfrac{sum sin A}{triangle }$
    $endgroup$
    – lab bhattacharjee
    Aug 25 '14 at 11:50












  • $begingroup$
    cant able to follow @labbhattacharjee
    $endgroup$
    – burm1
    Aug 25 '14 at 11:58










  • $begingroup$
    1/2 *base *height=area of triangle so you are saying p1= base and height =a?
    $endgroup$
    – burm1
    Aug 25 '14 at 11:59












  • $begingroup$
    rsummation sin a/triangle how
    $endgroup$
    – burm1
    Aug 25 '14 at 12:07










  • $begingroup$
    For future reference, you may take a look at this page to see how to format math on this site.
    $endgroup$
    – g.kov
    Feb 2 at 14:36
















1












$begingroup$


If P1, P2, P3 are altitudes of a triangle ABC from the vertices A, B, C and is the area of the triangle , then P^-1+P^-2+P^-3 is equal to






trigonometry







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    We have $dfrac12P_1cdot a=triangle$ etc. So, $sumdfrac1{P_1 }=dfrac{sum a}{2triangle}=Rdfrac{sum sin A}{triangle }$
    $endgroup$
    – lab bhattacharjee
    Aug 25 '14 at 11:50












  • $begingroup$
    cant able to follow @labbhattacharjee
    $endgroup$
    – burm1
    Aug 25 '14 at 11:58










  • $begingroup$
    1/2 *base *height=area of triangle so you are saying p1= base and height =a?
    $endgroup$
    – burm1
    Aug 25 '14 at 11:59












  • $begingroup$
    rsummation sin a/triangle how
    $endgroup$
    – burm1
    Aug 25 '14 at 12:07










  • $begingroup$
    For future reference, you may take a look at this page to see how to format math on this site.
    $endgroup$
    – g.kov
    Feb 2 at 14:36














1












1








1





$begingroup$


If P1, P2, P3 are altitudes of a triangle ABC from the vertices A, B, C and is the area of the triangle , then P^-1+P^-2+P^-3 is equal to






trigonometry







share|cite|improve this question









$endgroup$




If P1, P2, P3 are altitudes of a triangle ABC from the vertices A, B, C and is the area of the triangle , then P^-1+P^-2+P^-3 is equal to






trigonometry




trigonometry






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 25 '14 at 11:45









burm1burm1

6727




6727








  • 1




    $begingroup$
    We have $dfrac12P_1cdot a=triangle$ etc. So, $sumdfrac1{P_1 }=dfrac{sum a}{2triangle}=Rdfrac{sum sin A}{triangle }$
    $endgroup$
    – lab bhattacharjee
    Aug 25 '14 at 11:50












  • $begingroup$
    cant able to follow @labbhattacharjee
    $endgroup$
    – burm1
    Aug 25 '14 at 11:58










  • $begingroup$
    1/2 *base *height=area of triangle so you are saying p1= base and height =a?
    $endgroup$
    – burm1
    Aug 25 '14 at 11:59












  • $begingroup$
    rsummation sin a/triangle how
    $endgroup$
    – burm1
    Aug 25 '14 at 12:07










  • $begingroup$
    For future reference, you may take a look at this page to see how to format math on this site.
    $endgroup$
    – g.kov
    Feb 2 at 14:36














  • 1




    $begingroup$
    We have $dfrac12P_1cdot a=triangle$ etc. So, $sumdfrac1{P_1 }=dfrac{sum a}{2triangle}=Rdfrac{sum sin A}{triangle }$
    $endgroup$
    – lab bhattacharjee
    Aug 25 '14 at 11:50












  • $begingroup$
    cant able to follow @labbhattacharjee
    $endgroup$
    – burm1
    Aug 25 '14 at 11:58










  • $begingroup$
    1/2 *base *height=area of triangle so you are saying p1= base and height =a?
    $endgroup$
    – burm1
    Aug 25 '14 at 11:59












  • $begingroup$
    rsummation sin a/triangle how
    $endgroup$
    – burm1
    Aug 25 '14 at 12:07










  • $begingroup$
    For future reference, you may take a look at this page to see how to format math on this site.
    $endgroup$
    – g.kov
    Feb 2 at 14:36








1




1




$begingroup$
We have $dfrac12P_1cdot a=triangle$ etc. So, $sumdfrac1{P_1 }=dfrac{sum a}{2triangle}=Rdfrac{sum sin A}{triangle }$
$endgroup$
– lab bhattacharjee
Aug 25 '14 at 11:50






$begingroup$
We have $dfrac12P_1cdot a=triangle$ etc. So, $sumdfrac1{P_1 }=dfrac{sum a}{2triangle}=Rdfrac{sum sin A}{triangle }$
$endgroup$
– lab bhattacharjee
Aug 25 '14 at 11:50














$begingroup$
cant able to follow @labbhattacharjee
$endgroup$
– burm1
Aug 25 '14 at 11:58




$begingroup$
cant able to follow @labbhattacharjee
$endgroup$
– burm1
Aug 25 '14 at 11:58












$begingroup$
1/2 *base *height=area of triangle so you are saying p1= base and height =a?
$endgroup$
– burm1
Aug 25 '14 at 11:59






$begingroup$
1/2 *base *height=area of triangle so you are saying p1= base and height =a?
$endgroup$
– burm1
Aug 25 '14 at 11:59














$begingroup$
rsummation sin a/triangle how
$endgroup$
– burm1
Aug 25 '14 at 12:07




$begingroup$
rsummation sin a/triangle how
$endgroup$
– burm1
Aug 25 '14 at 12:07












$begingroup$
For future reference, you may take a look at this page to see how to format math on this site.
$endgroup$
– g.kov
Feb 2 at 14:36




$begingroup$
For future reference, you may take a look at this page to see how to format math on this site.
$endgroup$
– g.kov
Feb 2 at 14:36










2 Answers
2






active

oldest

votes


















0












$begingroup$

Using Area of Triangle in Terms of Side and Altitude formula,



$$triangle=frac12acdot P_1impliesfrac1{P_1}=frac a{2triangle}$$



$$implies sumfrac1{P_1}=frac{a+b+c}{2triangle}$$



Using Area of Triangle in Terms of Inradius formula, $$triangle=rcdot s$$



where $r$ is the inradius and $2s=a+b+c$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    summation 1/p2=a+b+c/2 triangle
    $endgroup$
    – burm1
    Aug 25 '14 at 13:03










  • $begingroup$
    @burm1, $$frac{a+b+c}2cdotfrac1{triangle}=scdotfrac1{rcdot s}=?$$
    $endgroup$
    – lab bhattacharjee
    Aug 25 '14 at 13:05












  • $begingroup$
    1/r .so 1/r+1/r+1/r =3/r
    $endgroup$
    – burm1
    Aug 25 '14 at 13:10










  • $begingroup$
    @burm1, have you noticed $sum ?$ It should be $dfrac1r$
    $endgroup$
    – lab bhattacharjee
    Aug 25 '14 at 13:11










  • $begingroup$
    yes i for get to include summation of 1/r.then summation of 3/r ?
    $endgroup$
    – burm1
    Aug 25 '14 at 13:13





















-2












$begingroup$

Using Area of triangle in terms of side and altitude formula,
Triangle= 1/2 a. P1=>1/p1=a/2triangle
=> £1/p1=a+b+c/2triangle



Using Area of triangle in terms of inradius formula,
Triangle= r.s
Where r is inradius and
2s=a+b+c
Hope it is useful......






share|cite|improve this answer









$endgroup$














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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    0












    $begingroup$

    Using Area of Triangle in Terms of Side and Altitude formula,



    $$triangle=frac12acdot P_1impliesfrac1{P_1}=frac a{2triangle}$$



    $$implies sumfrac1{P_1}=frac{a+b+c}{2triangle}$$



    Using Area of Triangle in Terms of Inradius formula, $$triangle=rcdot s$$



    where $r$ is the inradius and $2s=a+b+c$






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      summation 1/p2=a+b+c/2 triangle
      $endgroup$
      – burm1
      Aug 25 '14 at 13:03










    • $begingroup$
      @burm1, $$frac{a+b+c}2cdotfrac1{triangle}=scdotfrac1{rcdot s}=?$$
      $endgroup$
      – lab bhattacharjee
      Aug 25 '14 at 13:05












    • $begingroup$
      1/r .so 1/r+1/r+1/r =3/r
      $endgroup$
      – burm1
      Aug 25 '14 at 13:10










    • $begingroup$
      @burm1, have you noticed $sum ?$ It should be $dfrac1r$
      $endgroup$
      – lab bhattacharjee
      Aug 25 '14 at 13:11










    • $begingroup$
      yes i for get to include summation of 1/r.then summation of 3/r ?
      $endgroup$
      – burm1
      Aug 25 '14 at 13:13


















    0












    $begingroup$

    Using Area of Triangle in Terms of Side and Altitude formula,



    $$triangle=frac12acdot P_1impliesfrac1{P_1}=frac a{2triangle}$$



    $$implies sumfrac1{P_1}=frac{a+b+c}{2triangle}$$



    Using Area of Triangle in Terms of Inradius formula, $$triangle=rcdot s$$



    where $r$ is the inradius and $2s=a+b+c$






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      summation 1/p2=a+b+c/2 triangle
      $endgroup$
      – burm1
      Aug 25 '14 at 13:03










    • $begingroup$
      @burm1, $$frac{a+b+c}2cdotfrac1{triangle}=scdotfrac1{rcdot s}=?$$
      $endgroup$
      – lab bhattacharjee
      Aug 25 '14 at 13:05












    • $begingroup$
      1/r .so 1/r+1/r+1/r =3/r
      $endgroup$
      – burm1
      Aug 25 '14 at 13:10










    • $begingroup$
      @burm1, have you noticed $sum ?$ It should be $dfrac1r$
      $endgroup$
      – lab bhattacharjee
      Aug 25 '14 at 13:11










    • $begingroup$
      yes i for get to include summation of 1/r.then summation of 3/r ?
      $endgroup$
      – burm1
      Aug 25 '14 at 13:13
















    0












    0








    0





    $begingroup$

    Using Area of Triangle in Terms of Side and Altitude formula,



    $$triangle=frac12acdot P_1impliesfrac1{P_1}=frac a{2triangle}$$



    $$implies sumfrac1{P_1}=frac{a+b+c}{2triangle}$$



    Using Area of Triangle in Terms of Inradius formula, $$triangle=rcdot s$$



    where $r$ is the inradius and $2s=a+b+c$






    share|cite|improve this answer









    $endgroup$



    Using Area of Triangle in Terms of Side and Altitude formula,



    $$triangle=frac12acdot P_1impliesfrac1{P_1}=frac a{2triangle}$$



    $$implies sumfrac1{P_1}=frac{a+b+c}{2triangle}$$



    Using Area of Triangle in Terms of Inradius formula, $$triangle=rcdot s$$



    where $r$ is the inradius and $2s=a+b+c$







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Aug 25 '14 at 12:36









    lab bhattacharjeelab bhattacharjee

    228k15159279




    228k15159279












    • $begingroup$
      summation 1/p2=a+b+c/2 triangle
      $endgroup$
      – burm1
      Aug 25 '14 at 13:03










    • $begingroup$
      @burm1, $$frac{a+b+c}2cdotfrac1{triangle}=scdotfrac1{rcdot s}=?$$
      $endgroup$
      – lab bhattacharjee
      Aug 25 '14 at 13:05












    • $begingroup$
      1/r .so 1/r+1/r+1/r =3/r
      $endgroup$
      – burm1
      Aug 25 '14 at 13:10










    • $begingroup$
      @burm1, have you noticed $sum ?$ It should be $dfrac1r$
      $endgroup$
      – lab bhattacharjee
      Aug 25 '14 at 13:11










    • $begingroup$
      yes i for get to include summation of 1/r.then summation of 3/r ?
      $endgroup$
      – burm1
      Aug 25 '14 at 13:13




















    • $begingroup$
      summation 1/p2=a+b+c/2 triangle
      $endgroup$
      – burm1
      Aug 25 '14 at 13:03










    • $begingroup$
      @burm1, $$frac{a+b+c}2cdotfrac1{triangle}=scdotfrac1{rcdot s}=?$$
      $endgroup$
      – lab bhattacharjee
      Aug 25 '14 at 13:05












    • $begingroup$
      1/r .so 1/r+1/r+1/r =3/r
      $endgroup$
      – burm1
      Aug 25 '14 at 13:10










    • $begingroup$
      @burm1, have you noticed $sum ?$ It should be $dfrac1r$
      $endgroup$
      – lab bhattacharjee
      Aug 25 '14 at 13:11










    • $begingroup$
      yes i for get to include summation of 1/r.then summation of 3/r ?
      $endgroup$
      – burm1
      Aug 25 '14 at 13:13


















    $begingroup$
    summation 1/p2=a+b+c/2 triangle
    $endgroup$
    – burm1
    Aug 25 '14 at 13:03




    $begingroup$
    summation 1/p2=a+b+c/2 triangle
    $endgroup$
    – burm1
    Aug 25 '14 at 13:03












    $begingroup$
    @burm1, $$frac{a+b+c}2cdotfrac1{triangle}=scdotfrac1{rcdot s}=?$$
    $endgroup$
    – lab bhattacharjee
    Aug 25 '14 at 13:05






    $begingroup$
    @burm1, $$frac{a+b+c}2cdotfrac1{triangle}=scdotfrac1{rcdot s}=?$$
    $endgroup$
    – lab bhattacharjee
    Aug 25 '14 at 13:05














    $begingroup$
    1/r .so 1/r+1/r+1/r =3/r
    $endgroup$
    – burm1
    Aug 25 '14 at 13:10




    $begingroup$
    1/r .so 1/r+1/r+1/r =3/r
    $endgroup$
    – burm1
    Aug 25 '14 at 13:10












    $begingroup$
    @burm1, have you noticed $sum ?$ It should be $dfrac1r$
    $endgroup$
    – lab bhattacharjee
    Aug 25 '14 at 13:11




    $begingroup$
    @burm1, have you noticed $sum ?$ It should be $dfrac1r$
    $endgroup$
    – lab bhattacharjee
    Aug 25 '14 at 13:11












    $begingroup$
    yes i for get to include summation of 1/r.then summation of 3/r ?
    $endgroup$
    – burm1
    Aug 25 '14 at 13:13






    $begingroup$
    yes i for get to include summation of 1/r.then summation of 3/r ?
    $endgroup$
    – burm1
    Aug 25 '14 at 13:13













    -2












    $begingroup$

    Using Area of triangle in terms of side and altitude formula,
    Triangle= 1/2 a. P1=>1/p1=a/2triangle
    => £1/p1=a+b+c/2triangle



    Using Area of triangle in terms of inradius formula,
    Triangle= r.s
    Where r is inradius and
    2s=a+b+c
    Hope it is useful......






    share|cite|improve this answer









    $endgroup$


















      -2












      $begingroup$

      Using Area of triangle in terms of side and altitude formula,
      Triangle= 1/2 a. P1=>1/p1=a/2triangle
      => £1/p1=a+b+c/2triangle



      Using Area of triangle in terms of inradius formula,
      Triangle= r.s
      Where r is inradius and
      2s=a+b+c
      Hope it is useful......






      share|cite|improve this answer









      $endgroup$
















        -2












        -2








        -2





        $begingroup$

        Using Area of triangle in terms of side and altitude formula,
        Triangle= 1/2 a. P1=>1/p1=a/2triangle
        => £1/p1=a+b+c/2triangle



        Using Area of triangle in terms of inradius formula,
        Triangle= r.s
        Where r is inradius and
        2s=a+b+c
        Hope it is useful......






        share|cite|improve this answer









        $endgroup$



        Using Area of triangle in terms of side and altitude formula,
        Triangle= 1/2 a. P1=>1/p1=a/2triangle
        => £1/p1=a+b+c/2triangle



        Using Area of triangle in terms of inradius formula,
        Triangle= r.s
        Where r is inradius and
        2s=a+b+c
        Hope it is useful......







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Feb 2 at 14:15









        Tharuni chinniTharuni chinni

        1




        1






























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