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November 26th, 2010, 07:48 AM  #1 
Newbie Joined: Nov 2010 Posts: 5 Thanks: 0  concurrent triangles
Given an acute triangle ABC. A1,A2 are the points on the side BC; draw the square A1A2A3A4 (A3 is the point on the side CA; A4 is the point on the side AB). Ao is the intersection of A1A3 and A2A4. And Bo,Co is respectively the same. Prove that: AAo,BBo,CCo are concurrent.

November 26th, 2010, 02:44 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,485 Thanks: 2041 
Let points D, E and F lie outside the triangle ABC, such that triangles BDC, CEA and BAF are isosceles rightangled triangles whose hypotenuses are BC, CA and AB respectively. What you are asked to prove is equivalent to proving AD, BE and CF are concurrent. Both the equivalence and the concurrency can be established fairly easily using coordinate geometry. If you make an accurate diagram and persevere using classical geometrical methods, you should eventually find some rather elegant methods, constructions and results that make the tasks quite rewarding.

November 26th, 2010, 07:50 PM  #3 
Newbie Joined: Nov 2010 Posts: 5 Thanks: 0  Re: concurrent triangles
yep mate that surely helped thanks


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