Circumcenter : The point where the perpendicular bisectors of a triangle meet(D) and then taking this point as center of circle and joining these points to vertex of triangle,and then by taking either DA,DB,DC as radius and drawing a circle , we get circumcircle, and point D is called Circumcenter.
As given in the Question ,Out of given options, Circumcenter of triangle lies on the .... triangle,
We will answer by starting from option (1)
(A). Acute Angle Triangle : In acute angled triangle , circumcenter lies inside the triangle.
(B) Right Triangle: The two legs of right angled triangle meet at the vertex where the angle is of 90°.So from drawing perpendicular from the vertex where angle is of 90° to the hypotenuse gives you Circumcenter of right angled triangle.On Hypotenuse , Circumcenter of Right angle triangle lies.
So, Option (B) Right angled triangle, is correct option.
In Option (C) i.e in Obtuse angled triangle and in option (D) Equilateral Triangle , Circumcenter lies Outside and inside the triangle.(Images drawn below)
