The correct option is D)orthocenter. The point C in the figure is the orthocenter because it is the intersection point of the triangle's altitudes. Other special points like circumcenter, centroid, and incenter have different properties that are not evident in the image.
Point C in the triangle is the orthocenter. Here's why:
The orthocenter is the point where the altitudes of a triangle intersect. In the image, the lines CE, AG, and DB are labeled as altitudes. You can see that they all intersect at point C.
The circumcenter, centroid, and incenter are different special points in a triangle that have specific properties:
The circumcenter is the center of the circle that passes through all three vertices of the triangle. There is no such circle in the image, so C cannot be the circumcenter.
The centroid is the intersection point of the medians of the triangle. Medians are line segments drawn from each vertex to the midpoint of the opposite side. In the image, the medians are not shown, so we cannot determine if C is the centroid.
The incenter is the point where the angle bisectors of a triangle intersect. Angle bisectors are lines that divide each angle of the triangle into two congruent angles. There are no angle bisectors shown in the image, so we cannot determine if C is the incenter.
Therefore, based on the given information and the properties of different triangle centers, the only option that fits for point C is the orthocenter.