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Shtirlitz [24]
3 years ago
14

Find the center of the circle that you can circumscribe about DABC.

Mathematics
1 answer:
Vlada [557]3 years ago
5 0

The center of the circle that circumscribe about DABC is (h,k) = (1, 5).

A circle can be modelled after a expression of the form:

A\cdot x + B\cdot y + C =-x^{2}-y^{2} (1)

We can determine all coefficients by knowing three <em>distinct</em> points on plane.

If we know that (x_{1}, y_{1}) = (2, 8), (x_{2}, y_{2}) = (0, 8) and (x_{3}, y_{3}) = (2, 2), then the solution of the system of linear equations is:

2\cdot A + 8\cdot B + C = -68 (2)

8\cdot B + C = -64 (3)

2\cdot A + 2\cdot B + C = -8 (4)

A = -2, B = -10, C = 16

Now we proceed to <em>complete</em> squares and factor each resulting perfect square trinomial in order to determine the coordinates of the center of the circle:

x^{2}+y^{2}-2\cdot x -10\cdot y +16 = 0

(x^{2}-2\cdot x +1)-1+(y^{2}-10\cdot y +25)-25 +16 = 0

(x-1)^{2}+(y-5)^{2}= 10

The center of the circle that circumscribe about DABC is (h,k) = (1, 5).

To learn more on circles, we kindly invite to check this verified question: brainly.com/question/11833983

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