Circumcenter - Point of Concurrency of Perpendicular Bisectors
Consider any triangle with its vertices represented by three points in a coordinate system. Question is, can we find a point that is at the same distance from the vertices of the triangle? And if such a point exists then is it unique for that triangle or are there more such points? The answer to the first question is Yes. For any triangle, there exists a point in the plane of that triangle - inside or outside or lying on its edge - same distance away from the three vertices. This point is called the CIRCUMCENTER. Moreover, this point is unique for a given triangle, that is, a triangle has one and only one circumcenter. In △MNP, Point C is the circumcenter & CM = CP = CN For acute angled triangles, the circumcenter is always present INSIDE of the triangle, and conversely, if circumcenter lies inside of a triangle, the triangle is acute. For obtuse angled triangles, circumcenter is always present OUTSIDE of the triangle, and likewise, if the circumcenter is outs...