Relation between O,G,C

Q.

The figure formed by the lines $x^2+4xy+y^2=0$ and x - y = 4, is [Roorkee 1980]

1. A right angled triangle

2. An isosceles triangle

3. An equilateral triangle

4. None of these

Q. If the orthocenter and circumcentre of a triangle are (0, 0) and (3, 6) respectively then the centroid of the triangle is

1. (1, 2)
2. (2, 4)
3. 
4. 

Q. In triangle ABC, the equation of side BC is y=x. The centroid of Triangle ABC is (8, 3) and Circumcentre id (9, 3). if the circumradius of Triangle is R, then R/root 5 =

Q. If ($\alpha ,\beta$), $(\overline{x},\overline{y})and(u,v)$are respectively coordinates of the circumcentre, centroid and orthocentre of a triangle.

1. 3
2. 3
3. 3
4. 3

Q. 8. A circle of constant radius 2r passes through the origin and meets the axes in P and Q . locus of the centroid of the triangle POQ is

Q.

If a triangle has its orthocenter at (1, 1) and circumcenter at $(\frac{3}{2},\frac{3}{4})$ , then the coordinates of the centroid of the triangle are

1. 

2. 

3. 

4. 

Q. The vertices of an acute angled triangle are $A(x_1,x_1\tan \alpha ),B(x_2,x_2\tan \beta )$ and $C(x_3,x_2\tan \gamma ).$ If origin is the circumcentre of $△ABC$ and $H(a,b)$ be its orthocentre, then $\frac{b}{a}$ equals to
(where $x_1,x_2,x_3$ are positive)

1. $\frac{\cos \alpha +\cos \beta +\cos \gamma }{\cos \alpha \cos \beta \cos \gamma }$
2. $\frac{\sin \alpha +\sin \beta +\sin \gamma }{\sin \alpha \sin \beta \sin \gamma }$
3. $\frac{\tan \alpha +\tan \beta +\tan \gamma }{\tan \alpha \tan \beta \tan \gamma }$
4. $\frac{\sin \alpha +\sin \beta +\sin \gamma }{\cos \alpha +\cos \beta +\cos \gamma }$

Q. If the orthocenter of a triangle is $(6,3)$ and centroid is $(2,5)$, then find the circumcenter of the triangle.

1. $(1,2)$
2. $(1,3)$
3. $(0,5)$
4. $(0,6)$