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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

`(x_(1) + x_(2) + x_(3))/(x_(1) tan alpha + x_(2) tan beta + x_(3) tan gamma)`

B

`(x_(1) cos alpha + x_(2) cos beta + x_(3) cos gamma)/(x_(1)sinalpha + x_(2)sin beta +x_(3) sin gamma)`

C

`(tanalpha + tanbeta +tangamma)/(tan alpha. tanbeta . tan gamma)`

D

`(cosalpha+cosbeta+cosgamma)/(sinalpha+sinbeta+singamma)`

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A
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