7. Construct the incircle of ∆DEF in which DE = DF = 5.8 cm, ∠EDF = 65º.

Geometry Challenge: Constructing an Incircle

7. Construct the incircle of ∆DEF in which DE = DF = 5.8 cm, and ∠EDF = 65º.

Glossary of Terms

Incircle

The largest possible circle that can be drawn inside a triangle, touching all three sides without crossing them.

Triangle (∆)

A fundamental shape in geometry consisting of three straight sides and three angles.

Isosceles Triangle

A triangle that has two sides of equal length. In this problem, ∆DEF is isosceles because DE = DF.

Angle Bisector

A line or ray that divides an angle into two smaller, equal angles. The construction of an incircle relies on finding where these bisectors meet.

Incenter

The center point of a triangle's incircle. It is found at the intersection of the triangle's three angle bisectors.