The line segment joining $A(2, 2)$ and $B(2, -2)$ intersects $\ldots \ldots \ldots \ldots$

The points $A(2, 9)$,$B(a, 5)$,and $C(5, 5)$ are the vertices of a triangle $ABC$ right-angled at $B$. Find the value of $a$ and the area of $\triangle ABC$.

The coordinates of the centroid of a triangle having vertices $A(3, 2)$,$B(7, 5)$,and $C(2, 2)$ are:

Students of a school are standing in rows and columns in their playground for a drill practice. $A, B, C$ and $D$ are the positions of four students as shown in the figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students $A, B, C$ and $D$? If so,what should be his position?

If $D\left(\frac{-1}{2}, \frac{5}{2}\right)$,$E(7, 3)$,and $F\left(\frac{7}{2}, \frac{7}{2}\right)$ are the midpoints of the sides of $\triangle ABC$,find the area of $\triangle ABC$.

Find the circumcentre and circumradius of a triangle with vertices $(3,0), (-1,-6),$ and $(4,-1)$.