Br0card P0oints
The Brocard Point (which has a twin brother simply named The Second Brocard Point) is a simple but complex idea in geometry that French Mathematician, Henri Brocard, discovered.
In the simplest of words, it is a point (Q) in the triangle that, if an angle was made by drawing a line from the point Q, to a vertex and then another one, it would form a Brocard Angle.
A Brocard Angle just means that if one were to repeat the same process three times in the same triangle connecting the points in the same respective manner, all three angles would be congruent.
The Second Brocard Point is the point that would be found if one were to find the First Brocard Point using a backwards process. (In other words, you would be finding the three angles that are not identified on this geogebra file).
This point allows us to view a relationship between the triangle and three circles (each on tangent to each of the three sides, and passes through two vertices), the division of a triangle into smaller triangles with a corresponding angle, and the sides of triangles (their perpendicular bisectors and lines that run through vertices).
The FBP should not end up at vertex B of the triangle or should not be on the outside of the triangle. If you have configured the triangle in a manner that causes it to be, please reset the shape. (In other words, the triangle should always be read, Triangle CAB, ABC, or BCA clockwise.