Question

1. choose the correct answer.

the incenter is equidistant from each ___ of a triangle.
exterior
vertex
center
side

1. choose the correct answer.

the circumcenter of a(n) ___ triangle will be on the hypotenuse of the triangle.
acute
right
congruent
obtuse

Explanation:

• For the first question:
• The in - center of a triangle is the point of intersection of the angle bisectors of a triangle. By the property of the in - center, it is equidistant from each side of the triangle.
• The circum - center is equidistant from the vertices. The term “exterior” is not relevant in the context of the in - center's equidistant property. “Center” is too vague.
• For the second question:
• In a right - triangle, the circum - center (the point of intersection of the perpendicular bisectors of the sides) is the mid - point of the hypotenuse.
• In an acute triangle, the circum - center lies inside the triangle. In an obtuse triangle, the circum - center lies outside the triangle. “Congruent” is a property related to the equality of triangles, not the position of the circum - center.

Answer:

1. side
2. right