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The circumcenter of a triangle is the point at which three perpendicular bisectors from the triangle's sides overlap or meet. The circumcenter is the point of origin of a circumcircle, which is a circle inscribed inside a triangle.
The intersection of the perpendicular bisectors (i.e., the lines that are at right angles to the midpoint of each side) of all triangle sides yields the circumcenter. This signifies that the triangle's perpendicular bisectors are meeting at one point . Because all triangles are cyclic and may thus circumscribe a circle, each triangle has a circumcenter. Perpendicular bisectors of any two triangle sides are drawn to create the circumcenter of any triangle.
Let us look at some of the properties of a triangle's circumcenter:
Consider any ABC with O as the circumcenter.
Property 1: All of the triangle's vertices are equidistant from the circumcenter.
Property 2 : Isosceles triangles are produced by connecting O to the vertices.
When A is acute or when O and A are on the same side of BC, BOC = 2 A.
Property 4 : When A is obtuse or O and A are on opposite sides of BC, BOC = 2(180° - A).
Property 5: The location of the circumcenter varies depending on the kind of triangle.
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