Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 133Triangle, Angle Bisectors, Collinear Points. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
AE is an interior bisector of angle ABE/EC = AB/ACCD is an interior bisector of angle CAD/DB = AC/BCAE is an exterior bisector of angle BFA/FC = AB/BCthereforeBD/DA * AF/FC * CE/EB = BC/AC * AB/BC * AC/BC = 1thereforeD, E, F are collinear pointsMagdy Essafty
- P is on AC such that BP bisects <B.- It is known that P is the harmonic conjugate of F w/r AC.In conclusion, F-E-D must be colinear.