∴ Coordinates of A must be (cos‌α,sin‌α) Similarly, B=(cos‌β,sin‌β) and C=(cos‌γ,sin‌γ) Given, circumcentre coincides with origin and orthocentre lies on Y-axis. So, centroid must lie on Y-axis because circumcentre, orthocentre and centroid of any triangle always lies on the same line. ∵cos‌α+cos‌β+cos‌γ=0 ...(i) (because x-coordinate on Y-axis is zero)