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.