If the vertices of a triangle are $(0,0)$,$(6,0)$,and $(6,8)$,then its incentre will be:

If the coordinates of the vertices of triangle $ABC$ are $(6, 0)$,$(0, 6)$,and $(7, 7)$ respectively,find the circumcenter of the triangle.

Two vertices of a triangle $ABC$ are $A(3, -1)$ and $B(-2, 3)$,and its orthocentre is $P(1, 1)$. If the coordinates of the point $C$ are $(\alpha, \beta)$ and the centre of the circle circumscribing the triangle $PAB$ is $(h, k)$,then the value of $(\alpha + \beta) + 2(h + k)$ equals :

The coordinates of the orthocenter of the triangle whose sides are represented by the lines $L_1: 4x - 7y + 10 = 0$, $L_2: x + y - 5 = 0$ and $L_3: 7x + 4y - 15 = 0$ are...

The two vertices of a triangle are $(-1, 4)$ and $(5, 2)$. If its centroid is $(0, -3)$,find the third vertex.

Assertion $(A)$: If the centroid and circumcenter of a triangle are known,its orthocenter can be found.
Reason $(R)$: The centroid,orthocenter,and circumcenter of a triangle are collinear.