The circumcentre of a triangle having vertices `A(a,atan alpha),B(b,btan beta),C(c,ctan gamma)` is at origin, where`alpha+beta+gamma =pi`. Then the orthocentre lies on

If the centroid of a triangle with vertices (alpha, 1, 3), (-2, beta, -5) and (4, 7, gamma) is the origin then alpha beta gamma is equal to …..........

If the centroid of a triangle with vertices (alpha, 1, 3), (-2, beta, -5) and (4, 7, gamma) is the origin then alpha beta gamma is equal to …..........

If origin is the orthocentre of the triangle with vertices A(cos alpha,sin alpha),B(cos beta,sin beta),C(cos gamma,sin gamma) then cos(2 alpha-beta-gamma)+cos(2 beta-gamma-alpha)+cos(2 gamma-alpha-beta)=

Delta ABC has vertices A(a cos alpha,a sin alpha),B(a cos beta,a sin beta) and C(a cos gamma,a sin gamma) then its orthocentre is

The orthocentre of triangle formed by (a cos alpha,a sin alpha),(a cos beta,a sin beta),(a cos gamma,a sin gamma) is

The corodinates of the three vertices of a triangle are (a, a tan alpha) , (b ,b tan beta) and (c, c tangamma) . If the circumcentre and orthocentre of the triangle are at (0,0) and (h,k) respectively, prove that (h)/(k)=(cos alpha+ cos beta+ cos gamma)/( sin alpha+ sin beta + sin gamma) .