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

The vertices of a triangle are A(x_(1),x_(1)tan alpha),B(x_(2),x_(2)tan B eta) and C(x_(3),x_(3)tan gamma). If the circumcentre of Delta ABC coincides with the origin and H(a,b) be its orthocentre,then (a)/(b) is equal to

The vertices of a triangle are A(x_1,x_1tanalpha),(Bx_2,x_2tanbeta) and C(x_3,x_3tangamma) . If the circumcentre of triangle ABC coincides with the origin and H(a,b) be its orthocentre, then a/b is equal to

The vertices of a triangle are A(x_1, x_1, tan theta_1), B(x_2, x_2, tan theta_2) and C(x_3, x_3, tan theta_3). If the circumcentre coincides with origin then

The vertices of a triangle are (a, atan alpha ), B (b, beta ) and C (c, Ctan gamma ) . If the cicumcentre of DeltaABC coincides with the origin and H(bar(X) , bar(Y)) is the orthocentre, then show that bary/x=("Sin alpha + sinbeta+singamma)/(cosalpha+cosbeta+cosgamma)

The vertices of a triangle are A(x_(1),x_(1)tan theta_(1)),B(x_(2),x_(2)tan theta_(2))and C(x_(3),x_(3)tan theta_(3)) if the circumcentre of Delta ABC coincides with the origin and H(bar(x),bar(y)) is the orthocentre,show that (bar(y))/(bar(x))=(sin theta1+sin theta_(2)+sin theta_(3))/(cos theta_(1)+cos theta_(2)+cos theta_(3))

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 "Delta"A B C coincides with the origin and H( x , y ) is the orthocentre, show that y/( x )=(sintheta_1+ sintheta_2+sintheta_3)/(costheta_1+costheta_2+costheta_3)

The vertices of a triangle are : P(x_1,x_1 tan theta_1),Q (x_2, x_2tantheta_2) and R(x_3, x_3tantheta_3) . If the circumcentre of trianglePQR coincides with the origin and H(bar x,bar y) is the orthocentre, show that : bar y/bar x= (sintheta_1+sintheta_2+sintheta_3)/(costheta_1+costheta_2+costheta_3) .

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) .

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