Question

choose the term that best describes point p. orthocenter incenter centroid circumcenter

Explanation:

• Orthocenter: The orthocenter is the intersection of the altitudes of a triangle. There is no indication in the diagram that the lines are altitudes (perpendicular from a vertex to the opposite side for the purpose of forming altitudes in the traditional sense of orthocenter definition).
• Incenter: The incenter is the center of the inscribed circle (incircle) of a triangle. It is the point of intersection of the angle - bisectors of the triangle. In the diagram, we can see that \(P\) is equidistant from the sides of the triangle (as indicated by the perpendiculars \(PD\), \(PE\), \(PF\) which are radii of the inscribed circle) and \(P\) lies on the angle - bisectors (since the lines from the vertices \(A\), \(B\), \(C\) to \(P\) bisect the angles of the triangle).
• Centroid: The centroid is the intersection of the medians of a triangle (a median is a line segment joining a vertex to the mid - point of the opposite side). There is no indication in the diagram that the lines are medians.
• Circumcenter: The circumcenter is the center of the circumscribed circle (circumcircle) of a triangle. It is the point of intersection of the perpendicular bisectors of the sides of the triangle. There is no indication in the diagram that the lines are perpendicular bisectors of the sides.

Answer:

Incenter