In your own words, explain how to find the incenter and the circumcenter of a triangle and what the circumcenter theorem and incenter theorem tells us. (25 points)

Circumcenter is where three perpendicular bisectors intersect and incenter is where the three angle bisectors intersect.

Way to find them and the theorems are mentioned below.

Step-by-step explanation:

To find Incenter :

Construct angle bisectors of each angle of the triangle and their intersection  point gives the incenter.

To find Circumcenter:

Construct perpendicular bisectors of all sides of triangle and their intersection point gives the circumcenter.

Circumcenter Theorem: It states that the vertices of a triangle are equidistant from the circumcenter.

Incenter Theorem: It states that the incenter is equidistant from the sides of the triangle.

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2