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Find the circumcenter of the triangle ABC. A(4,3), B(6,-1), C(-2,-4). Please help I need to study and I don't know this.

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You should know that you may find the circumcenter of triangle using the perpendicular bisectors of triangle. The point of intersection of perpendicular bisectors represents the circumcenter of triangle.

Hence, you need to find the equations of two bisectors, at least.

You should know that perpendicular bisector of a side of triangle is a line that is perpendicular to the side and it cuts the side in two equal segments.

Since the problem provides informations that help you to find the slope and the midpoint, you need to use the point slope form of equation of bisector line such that: `y - y_M_1 = m_1*(x - x_M_1)` .

`M_1`  represents the midpoint of AB

You need to know the equation that relates the slopes of two perpendicular...

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