Answer: The length of the diameter of largest circle is 4 units and the co-ordinates of the center are (7, 8).
Step-by-step explanation: As shown in the attached figure below, two concentric circles C and C' are centered at the point O. AB is a diameter of the circle C' and TU is a diameter of the circle C.
The co-ordinates of the end-points of both the diameters are A(5, 8), B(9, 8), T(6, 8) and U(8, 8).
We are to find the length of the diameter of the largest circle C and the co-ordinates of the center O of the circles.
The length of diameter AB of the largest circle C can be calculated using distance formula as follows :
[tex]AB=\sqrt{(9-5)^2+(8-8)^2}=\sqrt{16+0}=\sqrt{16}=4~\textup{units}.[/tex]
Now, the center O will be the mid-point of the diameters AB and TU.
Therefore, the co-ordinates of O are
[tex]\left(\dfrac{5+9}{2},\dfrac{8+8}{2}\right)=(7, 8).[/tex]
Thus, the length of the diameter of largest circle is 4 units and the co-ordinates of the center are (7, 8)
