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

The vertices of a triangle are `A(x_1,x_1 tan alpha), B (x_2,x_2 tan Beta) and C(x_3, x_3 tan gamma)`. If the circumcentre of `DeltaABC` coincides with the origin and H (a, b) be its orthocentre, then `a/b` is equal to

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`G((x_1+x_2+x_3)/3,(x_1tanalpha+x_2tanbeta+x_3tangamma)/3)`
`H(3/2(x_1+x_2+x_3)/3,3/2(xtanalpha+x_2tanbeta+x_3tangamma)/3)`
`H(a,b)`
`sqrt(x_1^2+x_1^2tan^2alpha)=R`
`x_1^2=R^2/(sec^2alpha)`
`x_1=R/secalpha`
`a/b=(R(cosalpha+cosbeta+cosgamma))/(R(sinalpha+sinbeta+singamma))`.
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