Let tan α, tan β, tan γ; α, β, γ ≠ (2n - 1)π/2, n ∈ N be the slopes of three line segments OA, OB and OC,

Question

Let tan α, tan β, tan γ; α, β, γ ≠ \(\frac{(2n-1)\pi}{2},\) n ∈ N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of DABC coincides with origin and its orthocentre lies on y-axis, then the value of

\(\bigg(\frac{cos\,3\alpha + cos\,3\beta + cos\,3\gamma}{cos\,\alpha\,cos\,\beta\,cos\,\gamma}\bigg)^2\) is equal to :

Comments

Please explain why the centroid also lies on the y axis.

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Centroid, orthocentre and circumcenter are always collinear. Therefore centroid also lies on y axis.

Answer 1

Answer is (144)

Since orthocentre and circumcentre both lies on y-axis