a) inside the triangle EXPLANATION:Circumcenter of a triangle refers to a point which is equidistant from all THREE vertices of the triangle. As it is has equal DISTANCE from all the vertices we can draw a circle where all three vertices are on the circumference of the circle thus drawn.In the attachment, point O is the circumcenter of the triangle XYZ, here OX, OZ and OZ are radius of the circle, OY = OX = OZ.How to draw circumcenter of the acute angle ∆XYZ.Draw a perpendicular bisector of line XYDraw perpendicular bisector of line YZDraw a perpendicular bisector of line ZXFnd the point where all three perpendicular bisectors intersect each other, this is the circumcenter of the triangle XYZ.The ∆XYZ was an acute angle triangle, and we get its circumcenter inside the triangle.As we know, a point that lies on the perpendicular bisector of a line is equidistant from the both 2 end points of the same line. So, the circumcenter of a triangle will be equidistant from all three vertices. That's why we are able to draw a circle.if we apply the same construction then we would get to know :CIRCUMCENTRE of an acute angled triangle lies inside the triangle.Circumcentre of a right angled triangle lies on its hypotenuseCircumcentre of an obtuse angle triangle lies outside the triangle.Option a) inside the triangle is the CORRECT option.