Question

Question
Where is the circumcenter of this acute triangle located?

Responses

inside the triangle
inside the triangle

on a side of the triangle
on a side of the triangle

outside the triangle
outside the triangle

at a vertex of the triangle
at a vertex of the triangle
An acute triangle is drawn. All angles measures less than 90 degrees. No side of the acute triangle is either vertical or horizontal.

Answer 1

Inside the triangle.

Reason: the circumcenter is the intersection of the perpendicular bisectors of the sides (the center of the circumscribed circle). For an acute triangle those perpendicular bisectors meet at a point interior to the triangle. (By contrast, for a right triangle the circumcenter is the midpoint of the hypotenuse, and for an obtuse triangle it lies outside.)