What is the circumcenter of the triangle with vertices $(0, 0)$,$(3, 0)$,and $(0, 4)$?

The vertices of a triangle are $A(0,0), B(0,2)$ and $C(2,0)$. Find the distance between its orthocentre and circumcentre.

If $(2, 3)$,$(4, 5)$,and $(-2, 11)$ are the vertices of a triangle,what is the distance between the vertex $(4, 5)$ and the circumcenter?

What is the distance from the origin to the centroid of the triangle formed by the points $(1, 1)$,$(0, -7)$,and $(-4, 0)$?

If the orthocentre of the triangle,whose vertices are $(1,2), (2,3)$ and $(3,1)$ is $(\alpha, \beta)$,then the quadratic equation whose roots are $\alpha+4\beta$ and $4\alpha+\beta$ is:

Find the distance of the line $4x - y = 0$ from the point $P(4, 1)$ measured along the line making an angle of $135^{\circ}$ with the positive $x$-axis.