[Guest]

Triangular ABC and O point inside it, has given. Find E point on AB side, D point on BC side and F point on AC side, so that sum EO+OD+DF+FE reaches its minimum.

[Guest]

Points e and f coinciding with a.

d be the base of perpendicular from a.

[Guest]

Points e and f coinciding with a.

d be the base of perpendicular from a.

no random guess. need proof. answer is wrong btw

[hhh3]

let points E,D,&F be at middle of AB, BC & AC.... and O anywhere

in line joining E&D

not good in geomtry but anyway.....

[Guest]

E,F and D are the foot of the perpiduculars from point O.

which guarantees that OE,OF,OD are minimum.

Also FE will then be less(This will though depend on location of point O).

So i think for this situation the overall sum will be minimum.

[Guest]

E as B

D as C

F as A

Proof:

Max distance can be edges only....

[Guest]

Incomplete proof but answer and a beginning:

To determine shortest, break up the problem. Given O and F, to minimize FE+EO, the acute angle between FE and AB must equal the acute angle between AB and EO. Similarly, to minimize OD+DF, the acute angle between OD and BC must equal the acute angle between BC and DF. Position of F should be the point on AC from which a perpendicular passes through point O.

[Guest]

Incomplete proof but answer and a beginning:

To determine shortest, break up the problem. Given O and F, to minimize FE+EO, the acute angle between FE and AB must equal the acute angle between AB and EO. Similarly, to minimize OD+DF, the acute angle between OD and BC must equal the acute angle between BC and DF. Position of F should be the point on AC from which a perpendicular passes through point O.

Your on the right track. I highlighted wrong statements. And how could you find E point so that the acute angle between FE and AB equals the acute angle between AB and EO.

[Guest]

E as B

D as C

F as A

Proof:

Max distance can be edges only....

Its not true

[Guest]

use symmetry

[Guest]

Setting up your triangle so AC is your base the line FO would be perpendicular to AC and OD and OE are both parrallel to AC. Not sure how to prove it though.

[Guest]

Setting up your triangle so AC is your base the line FO would be perpendicular to AC and OD and OE are both parrallel to AC. Not sure how to prove it though.

u can't prove it becouse its wrong.