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P.T any triangle the perpendiculars from the vertices upon the opposite sides are concurrent?

P.T any triangle the perpendiculars from the vertices upon the opposite sides are concurrent?

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1 Answers

Badiuddin askIITians.ismu Expert
148 Points
11 years ago

Dear LINTA

let the vertics of triangle are a ,b,c  and point of intersection of two perpendicular from vertics to other side is H.

so  (a-b).( H-c) =0 

 or    a.H -a.c -b.H +b.c =0 ................1

 and        (b-c).(H-a) =0

  or    b.H - b.a -c.H +c.a =0 .............2


from equation 1 and 2nd   ,   1-2

 (c-a).(H-b) =0

so points are concurrent

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