Question

where do the points of concurrency of certain types of triangles lie? the circumcenter of an obtuse triangle lies the triangle. the incenter of a right triangle lies the triangle. the point of concurrency of the angle bisectors of an acute triangle lies the triangle. the point of concurrency that is equidistant from the vertices of a right triangle lies the triangle. inside on outside

Explanation:

1. The circum - center of an obtuse triangle is outside as the perpendicular bisectors of its sides intersect outside.
2. The in - center (point of concurrency of angle bisectors) of any triangle, including a right triangle, lies inside as it is the center of the inscribed circle.
3. The point of concurrency of angle bisectors (in - center) of an acute triangle lies inside as it is the center of the inscribed circle.
4. The point equidistant from the vertices of a right triangle is the circum - center which lies on the mid - point of the hypotenuse (i.e., on the triangle).

Answer:

1. outside
2. inside
3. inside
4. on