If the circumcenter of a triangle lies on the triangle then what type of triangle is it?

Solution:

In a triangle, we know that a circumcenter is a point that lies at the intersection of the perpendicular bisectors of the sides.

1. The circumcenter lies inside the triangle in an acute triangle.
2. The circumcenter lies outside the triangle in an obtuse triangle.
3. The circumcenter lies on the triangle at the midpoint of the hypotenuse in a right angled triangle.

Therefore, it is a right angled triangle.

If the circumcenter of a triangle lies on the triangle then what type of triangle is it?

Summary:

If the circumcenter of a triangle lies on the triangle then it is a right angled triangle.