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The vertices of a triangle are A(x1, x1t...

The vertices of a triangle are `A(x_1, x_1tantheta_1),B(x_2, x_2tantheta_2)a n dC(x_3, x_3tantheta_3)dot` if the circumcentre of `"Delta"A B C` coincides with the origin and `H( x , y )` is the orthocentre, show that ` y/( x )=(sintheta_1+s intheta_2+sintheta_3)/(costheta_1+costheta_2+costheta_3)`

A

`(cosalpha+cosbeta+cosgamma)/(cosalphacosbetacosgamma)`

B

`(sin alpha+sin beta+sin gamma)/(sin alphasin beta sin gamma)`

C

`(tan alpha+tan beta+tan gamma)/(tan alpha tan beta tan gamma)`

D

`(cos alpha +cos beta+cos gamma)/(sin alpha+sin beta+sin gamma)`

Text Solution

Verified by Experts

The correct Answer is:
D
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