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.
Circumcenter
The point where the perpendicular bisectors of the three sides of the triangle intersect
The incenter is the point of concurrency of the perpendicular bisectors of the triangle's sides
The orthocentre (where the perpendicular bisectors of the sides meet).
circumcenter
centroid
The three perpendicular bisectors (of the sides) of a triangle intersect at the circumcentre - the centre of the circle on which the three vertices of the triangle sit.
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 three ANGLE bisectors of a triangle also bisect the sides, and intersect at a point INSIDE the triangle. The angle bisectors are not necessarily perpendicular to them. The perpendicular bisectors of the sides can intersect in a point either inside or outside the triangle, depending on the shape of the triangle.
The perpendicular bisectors of the sides of a triangle intersect at its circumcentre.
Circumcenter. The circumcenter of a triangle is the center of the circumcircle of the triangle. It is the point, O, at which the perpendiculars bisectors of the sides of a triangle are concurrent. The circumcircle of a triangle is the circle that passes through the three vertices. Its center is at the circumcenter.
Yes. The orthocenter is the intersection of the altitudes; the circumcenter is the intersection of the perpendicular bisectors of the three sides of the triangle. The perpendicular bisector of and altitude to a given side are parallel, so they can coincide at the common center only if they are the same; that means that the opposite vertex is on the perpendicular bisector, so the other two sides are equal. Thus each pair of sides are equal, so the triangle is equilateral.
circumcenter
Circumcenter
The point where the perpendicular bisectors of the three sides of the triangle intersect
The incenter is the point of concurrency of the perpendicular bisectors of the triangle's sides