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

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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).
asked Mar 5, 2014 in GEOMETRY by payton Apprentice

1 Answer

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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).

answered Apr 15, 2014 by lilly Expert

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