SRL Archive - Mathematics

Funny Geometry problem

Markus

2010-01-10 09:15:40

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:


How can I construct P so that a triangle emerges?

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

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

Main

2010-01-10 11:37:28

What do you mean by construct p.

Bionicle

2010-01-10 12:17:57

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

Markus

2010-01-10 12:31:07

From: Main_Ftw
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.

From: bionicle1800
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

2010-01-10 16:07:32

This could be done with Thales no ?

Markus

2010-01-10 16:59:33

From: Dr D. Dervish
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

2010-01-11 13:58:25

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

Markus

2010-01-11 13:59:16

From: mixster
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

2010-01-11 15:30:05

Are the triangles equilateral?

Markus

2010-01-11 16:48:03

From: hubbard1989
Are the triangles equilateral?


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

g0tp0t

2010-03-22 16:08:54

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?