Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comment box below.Level: Mathematics Education, High School, Honors Geometry, College.Details: Click on the figure below.
Extend HF at G , G on AB. Join G to K, meet DE at P. From 1315 DP=NE =>PKN isoceles, => GKH isoceles
Dear AntonioCan this be proved directly without using Pr 1315?
https://goo.gl/photos/NtvVeEVnYmjzHqrLALet HF cut DB at L; LK and FA cut DE at N’ and GPer result of problem 1315 we haveDG=MNGM=NE , GN=ME=DM triangle FGM similar to FAK so GM= KA.(FM/FK)Triangle LDN’ similar to LAK so DN’= KA.( LN’/LK)= KA.(FM/FK)So GM= DN’=NE => MN=MN’Due to symmetry of LN’K to HNK over axis of symmetry BK => H,N ,K are collinear
Angle FHN=HNE=MNK, so they are colinear.
Please explain the reason of " HNE=MNK" in your solutionPeter Tran