ABC is an isosceles triangle with AB = AC. AB and AC are produced to E and F respectively such that BE * CF = AB^2. Show that EF passes through a fixed point.

Question

ABC is an isosceles triangle with AB = AC.  AB and AC are produced to E and F respectively such that BE * CF = AB^2.  Show that EF passes through a fixed point.

aum · Answer

By symmetry I would imagine the fixed point will be along the extended line of the altitude line from A to BC.

cwrw238 · Answer

yes

aum · Answer

|dw:1419618722964:dw|

ganeshie8 · Answer

*

aum · Answer

After spending way too much time on this problem I can only come up with an indirect proof for this problem. I did it in GeoGebra and uploaded it here: http://i.imgur.com/K63ivaD.png Clicking on the image will magnify the image a bit. Can anyone think of a direct proof based on the above proof?

aum · Answer

Analytical Geometry solution: http://prntscr.com/5mssor