Question

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)

Answer 1

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.

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.