The constructed circumcenter is attached and labelled as P.
The constructed incenter of a duplicate of the same triangle in 1 is attached and labelled as P.
What are incenter and circumcenter?
The incenter and circumcenter are points associated with triangles in geometry.
1. Incenter: The incenter is the point where the angle bisectors of a triangle intersect. An angle bisector is a line that divides an angle into two equal parts. In the case of a triangle, the incenter is the point where all three angle bisectors meet. The incenter is equidistant from the three sides of the triangle. This means that the incenter is the center of the inscribed circle (incircle), which is the largest circle that can fit inside the triangle. The incenter is often denoted by the letter "I" but we have labelled it as 'P'
2. Circumcenter: The circumcenter is the point where the perpendicular bisectors of a triangle's sides intersect. A perpendicular bisector is a line that is perpendicular to a side of a triangle and passes through its midpoint. For a triangle, the circumcenter is the point where all three perpendicular bisectors meet.
In summary, the incenter is related to the interior of the triangle and is the center of the inscribed circle, while the circumcenter is related to the exterior of the triangle and is the center of the circumscribed circle.