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If in a triangle ABC, sinA,sinB & sin C are in AP then the altitudes are in ? 1)AP 2)GP 3)HP 4)none

If in a triangle ABC, sinA,sinB & sin C are in AP then the altitudes are in ?
1)AP
2)GP
3)HP
4)none

Grade:12

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
Vikas TU
14149 Points
one year ago
p1, p2 , p3 are the altitudes from A , B , C respectively.
del = .5ap2=.5bp2=.5cp3
p1 = 2del / a 
p2 = 2del/b 
p3 = 2del/c 
Apply sine law, 
p1 = 2del/KsinA ,
p2 = 2del/KsinB 
p3 = 2del/KsinC 
Sin A , SinB , SinC are in AP 
so, p1, p2, p3 are in HP 

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