Where Is the Circumcenter of an Equilateral Triangle

If any of the incenter orthocenter or centroid coincide with the circumcenter of a triangle then it is called an equilateral triangle. This page shows how to construct an equilateral triangle with compass and straightedge or ruler.

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Here the circumcircle passes through all the three vertices of the triangle.

. The orthocenter the centroid and the circumcenter of a non-equilateral triangle are aligned. The reason is the other two angles and sides are still unknown. Well we cannot answer a right-angled triangle with only the hypotenuse C.

It begins with a given line segment which is the length of each side of the desired equilateral triangle. The circumcenter of equilateral triangle is the point of intersection perpendicular bisectors of the sides. Therefore the right triangle still has many forms.

It means that they lie on the same straight line called a line of Euler. This online hypotenuse calculator is functioned to determine the length of any side of a right-angled triangle. It works because the compass width is not changed between drawing each side guaranteeing they are all congruent same length.

It is similar to the 60 degree angle. You can see in the below figure that the orthocenter centroid and circumcenter all are lying on the same straight line and are represented by O G and H.

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