Question

Concentric circles are drawn in the coordinate plane. A diameter is drawn in the small circle and in the large circle, and the endpoints of the two diameters are at A(5, 8), B(9, 8), T(6, 8), and U(8, 8). Determine the length of the diameter of the largest circle and the center of the circles

Answer 1

A(5,8) T(6, 8 5(8 1(0, U(88 5(8,meters and length of the circle So 2 units of the circle = (7,8 C. width :)

Answer 2

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 :

`AB=√((9-5)^2+(8-8)^2)=√(16+0)=√(16)=4~\textup{units}.`

Now, the center O will be the mid-point of the diameters AB and TU.

Therefore, the co-ordinates of O are

`\left((5+9)/(2),(8+8)/(2)\right)=(7, 8).`

Thus, the length of the diameter of largest circle is 4 units and the co-ordinates of the center are (7, 8)