My Math Forum concurrent triangles

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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: 20,921 Thanks: 2203 Let points D, E and F lie outside the triangle ABC, such that triangles BDC, CEA and BAF are isosceles right-angled 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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