Inscribing and circumscribing circles on a triangle

The  exercise appears under the Geometry Math Mission. This exercise practices formal geometric construction with the straightedge and compass.

Types of Problems
There is one type of problem in this exercise:


 * 1) Construct the geometric object: This problem asks the student to use a compass and straightedge to construct a particular geometric object.Iaccoat1.png

Strategies
Knowledge of loci of points and some familiarity with geometric construction tools are encouraged to ensure success on this exercise.
 * 1) The inscribed triangle is centered at the intersection of the angle bisectors of the angles, also called an incenter.
 * 2) The circumscribed triangle is centered at the intersection of the perpendicular bisectors of the sides, also called a circumcenter.
 * 3) The other famous centers are the centroid or center of mass, where the medians of the triangle intersect, and the orthocenter, where the altitudes intersect.

Real-life Applications

 * 1) Straightedge and compass construction were the foundation of mathematics for thousands of years.