If you have enjoyed the wonders and beauty of mathematics shown in this blog, here are some addition for you to appreciate it more. Below are some of the most amazing facts about triangles.

1. The three altitudes of meet at a common point. This point is called the **orthocenter** of the triangle.

2. The three lines from each vertex to the midpoint of the opposite side also meet at a common point called **centroid** of the triangle.

3. The lines that pass through the midpoint of each side and is perpendicular to the side (the perpendicular bisector) also meet at a common point called the **circumcenter** of the triangle.

4. The circumcenter is the center of the circle passing through the three vertices of the triangle. This circle is called the **circumcircle**.

5. The orthocenter, the centroid, and the circumcenter of a triangle line on a straight line. This line is called the **Euler line**. The line was named after the great mathematician Leonhard Euler.

These are only a few of the many amazing properties of triangles. Now the question is, is this true for all types of triangles? You might need a Geometry software to answer this question. You might want to try GeoGebra (it’s for free) and learn about it in my step by step tutorials.

One more thing, on the Euler’s line, the distance from the centroid to the circumcentre is half that from the centroid to the orthocentre. Fascinating, isn’t it?

Thank you Sohael. Yes, I will include that in the revision later.

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If Sohael Babwani’s statement is number six then

Fact 7: The three bisectrices meet in a point, what name does it have?

Fact 8: It is the centre of the innner circle, because it has the the same distance to all three edges.Sohael Babwani

Thanks Markus.