Question

what is Euler line? explain properly and answer only if you are absolutely sure about it. otherwise I will have to report.​

Answer 1

Answer:

In geometry, the Euler line, named after Leonhard Euler (/ˈɔɪlər/), is a line determined from any triangle that is not equilateral. It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.[1]

Euler's line (red) is a straight line through the centroid (orange), orthocenter (blue), circumcenter (green) and center of the nine-point circle (red).

The concept of a triangle's Euler line extends to the Euler line of other shapes, such as the quadrilateral and the tetrahedron.

Answer 2

Answer:

In geometry, the Euler line, named after Leonhard Euler (/ˈɔɪlər/), is a line determined from any triangle that is not equilateral.

Well, Eulers line is quite popular when one is dealing with geometry. Its a special line in the plane of the triangle that passes through many important well known points and thus proving all those points to be collinear. Collinearity of points is very useful in solving certain complex pure geometry problems. Hence special line such as Eulers line are of great help to Mathematicians.

Eulers line passes through centroid (the intersection point of the three medians), orthocentre (the intersection point of perpendiculars drawn from each vertex), circumcentre (the intersection point of perpendicular bisectors of the sides), Exeter point, and the centre of the nine-point circle.

The red line up in the figure represents the Eulers line.

It's also known that the centroid divides the line segment joining orthocentre and circumcentre in the ratio 2:1 and this is a well known result and can be found in problems on vectors, coordinate geometry and more commonly in pure geometry. Well, this is not what you asked but I just felt like sharing it..

I hope it might help you

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