A vertex.
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The right angle is formed by the intersection of the triangle's "legs".
A right triangle. See: http://en.wikipedia.org/wiki/Circumscribed_circle#Circumscribed_circles_of_triangles
The common intersection of the angle bisectors of a triangle is called the incenter. It is the center of the inscribed circle of the triangle, and is equidistant from the three sides of the triangle.
The point equidistant from the three sides of a triangle is the center of the triangle. The center of the triangle is the point of intersection of the medians of the triangle. The medians of a triangle are the line segments that join the vertices of the triangle to the midpoints of the opposite sides.
The point of intersection of two sides of a polygon is called a vertex. A vertex describes the intersection or corners of a shape.