Funny Geometry problem

[Markus]

Imagine you got an acute-angled triangle ABC. At one side you put a point P, and then you draw right-angled lines like this:

http://i45.tinypic.com/xcrr6h.png

How can I construct P so that a triangle emerges?
http://i50.tinypic.com/254yqhh.png

Allowed stuff: compass and ruler.
Needed stuff: ruler, and something to do a right angle.

Took me over 4 weeks to find it (yes I got it finally!), lets see if SRL can do it faster :p

Edit: you also need to proove your solution. The prize: the fact that you did something you can't seem to find on Google :D

Update: I'm going to give three hints, the same ones my maths teacher gave me: Highlight to view


Look for similar triangles
For the algebraic solution: ebook3000.com/Topics-in-Elementary-Geometry_24063.html, chapter 15 (A Closure Problem for Triangles)
http://i48.tinypic.com/107qrrl.png

[Main]

What do you mean by construct p.

[Bionicle]

Well im not sure what your saying...
erase the line, and redraw it? O_o
explain further please :p

[Markus]

What do you mean by construct p.
That you can pinpoint P exactly at a given triangle, so that a triangle like in the second pic appears.


Well im not sure what your saying...
erase the line, and redraw it? O_o
explain further please :p

Can't say it more detailed. Just take a look at the pics to see what I want :)

[Dervish]

This could be done with Thales no ?

[Markus]

This could be done with Thales no ?

Tried it but couldn't find out the right way to do it. But if you can find out how to do it, give it a shot! :)

[mixster]

I have found the solution method and now Markus is forcing me to post, most likely to bump this up!

[Markus]

I have found the solution method and now Markus is forcing me to post, most likely to bump this up!

My evil plan is discovered :(

[hubbard1989]

Are the triangles equilateral?

[Markus]

Are the triangles equilateral?

No, maybe in the pics it looks like one, but it can be any acute triangle.

[g0tp0t]

by equilateral did he mean all 3 outside triangles are congruent or just the middle being equilateral.

My question is are all 3 of the outer triangles congruent and is the center triangle equilateral?