Question

the point where the perpendicular bisectors of a triangle intersect is called the:
a. centroid
b. incenter
c. orthocenter
d. circumcenter

in which type of triangle is the incenter also the circumcenter?
a. obtuse triangle
b. scalene triangle
c. equilateral triangle
d. right triangle

which point of concurrency is equidistant from all three vertices of a triangle?
a. centroid
b. incenter
c. circumcenter
d. orthocenter

Explanation:

1. The point where the perpendicular bisectors of a triangle intersect is the circum - center by definition.
2. In an equilateral triangle, due to its symmetry, the in - center (point of intersection of angle bisectors) and the circum - center (point of intersection of perpendicular bisectors) coincide.
3. The circum - center is equidistant from all three vertices of a triangle as it is the center of the circum - circle that passes through the vertices.

Answer:

1. d. Circumcenter
2. c. Equilateral triangle
3. c. Circumcenter