Problem
GEO-B2-M06-P011 Angle Bisectors
#11
★★★☆☆ Level 3 of 5
Use Ceva's theorem to prove that the internal angle bisectors of a triangle are concurrent.
Use the angle bisector theorem.
Let the angle bisectors from \(A,B,C\) meet the opposite sides at \(D,E,F\). Then \(\frac{BD}{DC}=\frac{AB}{AC}\), \(\frac{CE}{EA}=\frac{BC}{BA}\), \(\frac{AF}{FB}=\frac{CA}{CB}\). The product of these three ratios is \(1\). By Ceva, the angle bisectors are concurrent.
A good connection between two basic theorems.