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

Would assume end point points of diameter of first cirlce

=a(5, 8), b(9, 8)

Length of diameter is the distance between the two points.

d = √( (9 - 5)² + (8 - 8)²)

d = √(4² + 0²)

d =√(4²) = 4 units.

diameter of first circle = 4 units.

Centre is the midpoint between the coordinates  (5, 8) and (9, 8)

Midpoint = ((5+9)/2  , (8+8)/2) = (14/2 , 16/2) = (7, 8) 

Second circle:

=a(5, 8), b(9, 8)

Length of diameter is the distance between the two points.

d = √( (9 - 5)² + (8 - 8)²)

d = √(4² + 0²)

d =√(4²) = 4 units.

diameter of first circle = 4 units.

Centre is the midpoint between the coordinates  (5, 8) and (9, 8)

Midpoint = ((5+9)/2  , (8+8)/2) = (14/2 , 16/2) = (7, 8) 

Second circle:
=a(5, 8), b(9, 8)

Length of diameter is the distance between the two points.

d = √( (9 - 5)² + (8 - 8)²)

d = √(4² + 0²)

d =√(4²) = 4 units.

diameter of first circle = 4 units.

Centre is the midpoint between the coordinates  (5, 8) and (9, 8)

Midpoint = ((5+9)/2  , (8+8)/2) = (14/2 , 16/2) = (7, 8) 

Second circle:

t(6, 8), u(8, 8)

Length of diameter is the distance between the two points.

d = √( (8 - 6)² + (8 - 8)²)

d = √(2² + 0²)

d =√(2²) = 2 units.

diameter of second circle = 2 units.

Centre is the midpoint between the coordinates  (6, 8) and (8, 8)

Midpoint = ((6+8)/2  , (8+8)/2) = (14/2 , 16/2) = (7, 8)

The centre of second circle is (7,8) which is the same as first and from the question it says the circles are concentric meaning having the same centre.

So length of diameter of first circle = 4 units, second circle = 2 units
centre = (7, 8).

I hope this helped.   

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