Let's locate each point of concurrency and see if it is in the blue peg.
Circumcenter
According to the definition, a circumcenter of a triangle is a point of intersection of the triangle's perpendicular bisectors. Let's draw three perpendicular bisectors in the triangle and locate their point of intersection.
Incenter
Let's recall that an incenter of a triangle is a point of intersection of the triangle angle bisectors. Hence, to find the incenter of the triangle we need to draw three angle bisectors.
Centroid
A centroid of a triangle is a point of intersection of the triangle medians. Let's draw three medians of our triangle and find their point of intersection.
Orthocenter
Let's review that an orthocenter of a triangle is a point of intersection of the triangle altitudes. Thus, to locate the orthocenter of the triangle, we will draw three altitudes.
Concludion
As we can see, a circumcenter, incenter, centroid, and orthocenter of an equilateral triangle are located at the same point, which is in the center of the blue peg. Therefore, the blue peg represents all four points of concurrency.
