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 `DeltaABC` coincides with the origin and `H( barx , bary )` is the orthocentre, show that ` bary/( barx )=(sintheta1+sintheta_2+sintheta_3)/(costheta_1+costheta_2+costheta_3)`

Explanation

When circumcentre is origin

`∴OA ^2 =OB ^2=OC ^2`



`x_1^2 + x_1^2 tan^2 θ_1 =`
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`x_2^2 + x_2^2 tan^2 θ_2 =`

`x_3^2 + x_3^2 tan^2θ_3 = r^2`
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