Math Snap

STEP 1

1. We are given a triangle with point C marked inside.
2. Angle bisectors from each vertex intersect at point C.
3. We need to classify point C as one of the following: Circumcenter, Incenter, Centroid, or Orthocenter.

STEP 2

1. Understand the definitions of Circumcenter, Incenter, Centroid, and Orthocenter.
2. Analyze the given information about point C.
3. Classify point C based on the analysis.

STEP 3

Understand the definitions:
- Circumcenter: The point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from the vertices of the triangle.
- Incenter: The point where the angle bisectors of a triangle intersect. It is equidistant from the sides of the triangle.
- Centroid: The point where the medians of a triangle intersect. It is the center of mass of the triangle.
- Orthocenter: The point where the altitudes of a triangle intersect.

STEP 4

Analyze the given information:
- The image description states that angle bisectors from each vertex intersect at point C.

Classify point C:
- Since point C is the intersection of the angle bisectors, it is the Incenter of the triangle.
The classification of point C is:
$$\boxed{\text{Incenter}}$$