Property 3: For a triangle whose ∠A is acute or when O and A are on the same side of BC, ∠BOC = 2 ∠A.Property 2: The triangles that are formed by joining the circumcenter O to the vertices are isosceles triangles.Property 1: All the vertices of a triangle are at an equal distance from the circumcenter i.e AO = BO = CO.Let us consider a triangle ABC whose circumcenter is denoted by O as shown in the figure. The following are the properties of the circumcenter of the triangle. Read More: Centroid of a Triangle: Properties, Formula, Derivation, Theorem The circumcenter of an acute triangle is located within the form, but the circumcenter of an obtuse triangle is located outside the triangle. Perpendicular bisectors of any two sides of a triangle are drawn to create the circumcenter of any triangle. Since all triangles are cyclic and can circumscribe a circle, they all have a circumcenter. This indicates that the triangle's perpendicular bisectors are concurrent (i.e. The intersection of the perpendicular bisectors (i.e., the lines that are at right angles to the midpoint of each side) of all sides of a triangle yields the circumcenter of the triangle. The circumcircle and consequently the circumcenter can only be found in regular polygons, triangles, rectangles, and right-kites. A circumcircle is not necessary to be present for all polygons. Cyclic polygons are all polygons that have circumcircles.
The circumcircle of a polygon is the circle that passes through all of its vertices and the centre of that circle is called the circumcenter. The circumcenter is the centre point of the circumcircle drawn around a polygon.
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