Question

identifying the incenter of a triangle
which triangle shows the incenter at point a?

Explanation:

The incenter of a triangle is the point where the angle bisectors of the triangle intersect. To identify the triangle with incenter at point A, we need to check which triangle has point A at the intersection of its angle bisectors (marked by angle - arc symbols or the property of angle bisectors). The second triangle (from the left) has markings that indicate angle bisectors intersecting at point A, which is consistent with the definition of the incenter (the intersection of angle bisectors). The other triangles have markings related to perpendicular bisectors (for circumcenter) or other segment bisectors, not angle bisectors.

Answer:

The second triangle (from the left) with point A at the intersection of angle - bisecting lines (marked by arc - like angle markings)