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(A) The given lines are $L_1: x + y - 5 = 0$,$L_2: x - y + 1 = 0$,and $L_3: y - 1 = 0$.Note that the slopes of $L_1$ and $L_2$ are $m_1 = -1$ and $m_2

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$(2, 1)$

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(A) The given lines are $L_1: x + y - 5 = 0$,$L_2: x - y + 1 = 0$,and $L_3: y - 1 = 0$.Note that the slopes of $L_1$ and $L_2$ are $m_1 = -1$ and $m_2 = 1$. Since $m_1 	imes m_2 = -1$,the lines $L_1$ and $L_2$ are perpendicular.Thus,the triangle is a right-angled triangle,and the hypotenuse is the line segment connecting the intersection points of $L_3$ with $L_1$ and $L_2$.Intersection of $L_1$ and $L_3$: $x + 1 - 5 = 0 \implies x = 4$. Point $A = (4, 1)$.Intersection of $L_2$ and $L_3$: $x - 1 + 1 = 0 \implies x = 0$. Point $B = (0, 1)$.The circumcenter of a right-angled triangle is the midpoint of the hypotenuse.Midpoint of $AB = (\frac{4+0}{2}, \frac{1+1}{2}) = (2, 1)$.

If the sides of a triangle are given by the equations $x + y - 5 = 0$,$x - y + 1 = 0$,and $y - 1 = 0$,then what is its circumcenter?

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