Question

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

Answer 1

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 distinct 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 complete 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