Question

Determine whether each statement is true or false.(4 points)
True False
When you construct an inscribed circle of a triangle, the point where the three angle bisectors intersect is called the incenter.


When a circle is inscribed in a triangle, each side of the triangle is perpendicular to the radius of the circle.


When you construct a circumscribed circle around a triangle, the intersection of the perpendicular bisectors create a centroid.


In a circle circumscribed about a triangle, the distance from any vertex to the circumcenter is congruent.

Answer 1

True — When you construct an inscribed circle of a triangle, the point where the three angle bisectors intersect is called the incenter.

True — For an incircle, each side of the triangle is tangent to the circle, and the radius to the point of tangency is perpendicular to that side.

False — The intersection of the perpendicular bisectors is the circumcenter, not the centroid (the centroid is the intersection of the medians).

True — In a circumcircle, all vertices are the same distance from the circumcenter (that common distance is the circumradius).