What is the nature of the center of gravity of a triangle

What is the nature of the center of gravity of a triangle

What is the nature of the center of gravity of a triangle
The distance from the center of gravity of a triangle to the midpoint of the opposite side is equal to one third of the length of the center line on that side

Making triangles
Xiaoying wants to make a triangle with wooden sticks. Now she has two wooden sticks of 30cm and 50cm in length. How long should the third wooden stick she is looking for be? Explain why

The length of the third stick should be less than 80cm and more than 20cm
Reason: the sum of the two sides of a triangle is less than the third side, and the difference between the two sides is greater than the third side

A circle made of triangles
We know the triangle ABC and make a circle of ABC

First of all, triangle ABC and triangle ABC are different. In geometry, uppercase letters are used to represent points and lowercase letters are used to represent edges~
Given the triangle ABC, we have made a circle of ABC, which means that the distance from the center of the circle to the three points of ABC is equal, so the center of the circle is the intersection of the three sides of the triangle's middle perpendicular, that is, the outer center of the triangle. The radius length is the distance from the outer center to ABC. Can the middle perpendicular do it?