Centroid, Incentre and Circumcentre and Orthocentre of a Triangle - Practice Questions & MCQ

Which centre of triangle is the balance point of the triangle ? 

If the vertices of a triangle are rational points, which of the following point(s) of the triangle is (are) always rational point(s)?

The coordinates of the middle points of the sides of a triangle are and  then the coordinates of its centroid is:

If circumcenter , centroid , orthocenter and incenter of a triangle coincide , then the triangle is 

If circumcenter , orthocenter centroid and incenter lie on the same line , but not coincide the triangle is 

If the circumcenter and orthocenter of a triangle are points: 

$O(2,13/8)$ and $H(3,3/4)$ respectively then centroid of triangle 

Centroid of the triangle with vertices (0,0,0), (2,3,4) and (p,q,r) is (1,2,3) then p+q+r equals 

If orthocentre and circumcentre  of a $\mathrm{△}$ are respectively (1,1) and (3,2) , then the coordinates of its  centroid  are 

Let $\overrightarrow{P}$ is the p.v of the orthocentre and $\overrightarrow{g}$ is the p.v of the centroid of the triangle ABC, where circumcentre is the origin. If $\overrightarrow{P}=K\overrightarrow{g}thenK$

What is the equation of the median of $\mathrm{△}ABC$?