Question

what is the point where the medians of a triangle intersect? a. centroid b. circumcenter c. orthocenter d. incenter what is the key property of the circumcenter in an acute triangle? a. it can be inside, outside, or on the triangle, depending on the type of triangle. b. it is always inside the triangle. c. it is always outside the triangle. d. it is always on the triangle. which point of concurrency would be used to place a water tower equidistant from three towns? a. centroid b. incenter c. circumcenter d. orthocenter

Explanation:

1. The centroid is defined as the point of intersection of the medians of a triangle.
2. The circum - center of an acute triangle is always inside the triangle. For an obtuse - angled triangle, it is outside, and for a right - angled triangle, it is on the hypotenuse.
3. The circum - center is the point that is equidistant from the three vertices of a triangle. Placing a water tower at the circum - center of the triangle formed by three towns would make it equidistant from the three towns.

Answer:

1. a. Centroid
2. b. It is always inside the triangle.
3. c. Circumcenter