Determine the length of the diameter of the largest circle and the center of the circle

Question

concentric circles are drawn in the coordinate plane. A diameter is drawn in the small circle and in the large corcle, and the end points of two diameters are at A(5,8) B(9,8) T(6,8) and U(8,8).

Answer 1

Given :

AB is a diameter of large circle, and TU is a diameter of small circle.

The points are A(5, 8), B(9, 8), T(6, 8), and U(8, 8).

Observe the above diagram,

Length of the diameter of the largest circle = Distance between the points T and U.

= sqrt [ (8 - 6)^2 + (8 - 8)^2 }

= sqrt ( 2^2 + 0^2 )

= sqrt ( 4 + 0 )

= 2 units.

The center of the circle = mid point of TU (or) mid point of AB.

= [(6 + 8)/2, (8 + 8)/2]

= (14 / 2, 16 / 2)

= (7, 8).

Therefore, the length of the diameter of the largest circle is 2 units, and the center of the circle is (7, 8).