Problem 126. Incenter of a Triangle, Angle Bisector, Proportions.
Level: High School, College, SAT Prep.

In the figure below, given a triangle ABC of sides AB = c, BC = a, and AC = b. Let be BD the angle bisector of A, I the incenter, BI = e and ID =d. Prove that: . Post a comment. 

 

FACTS AND HINTS:

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

See: Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem.