bonanova Posted March 11, 2013 Report Share Posted March 11, 2013 Warm-up problem: Bisect the angles of a triangle. Describe the point(s) where each bisector first intersects one of the others. Now try this: Trisect the angles of a triangle. Describe the points where each trisector first intersects one of the others. Quote Link to comment Share on other sites More sharing options...

0 kukupai Posted March 14, 2013 Report Share Posted March 14, 2013 ... this triangle is equilateral. (If my drawing was correct.) Quote Link to comment Share on other sites More sharing options...

0 Debasis Posted March 11, 2013 Report Share Posted March 11, 2013 Do we have to name that point?if we have to name then the angle bisectors of a triangle meet at the incentre (i learned about it in school) and i dont know about the point where trisection meet.....i do hope you want us to find coordinates of the point... Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted March 11, 2013 Author Report Share Posted March 11, 2013 Do we have to name that point?if we have to name then the angle bisectors of a triangle meet at the incentre (i learned about it in school) and i dont know about the point where trisection meet.....i do hope you want us to find coordinates of the point... You're right about the bisector case. But for the trisector case there is more than one point. In fact there are three places where a trisector of one angle first intersects a trisector of one of the other angles. And there is something special about those three points. Quote Link to comment Share on other sites More sharing options...

0 Debasis Posted March 12, 2013 Report Share Posted March 12, 2013 Do we have to name that point?if we have to name then the angle bisectors of a triangle meet at the incentre (i learned about it in school) and i dont know about the point where trisection meet.....i do hope you want us to find coordinates of the point... You're right about the bisector case. But for the trisector case there is more than one point. In fact there are three places where a trisector of one angle first intersects a trisector of one of the other angles. And there is something special about those three points. the three point where the trisectors meet lie on the same line... Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted March 14, 2013 Author Report Share Posted March 14, 2013 Do we have to name that point?if we have to name then the angle bisectors of a triangle meet at the incentre (i learned about it in school) and i dont know about the point where trisection meet.....i do hope you want us to find coordinates of the point... You're right about the bisector case. But for the trisector case there is more than one point. In fact there are three places where a trisector of one angle first intersects a trisector of one of the other angles. And there is something special about those three points. the three point where the trisectors meet lie on the same line... Actually they are not collinear. That being the case, they form a triangle. So the OP really asks: what is special about the triangle formed by these three points? Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted March 15, 2013 Author Report Share Posted March 15, 2013 (edited) ... this triangle is equilateral.(If my drawing was correct.) Correct. Good job. I wonder if there is a proof of this that is not overly complex? Edit: Well, No. I just found the proof, and it's not beautiful for its simplicity. You start with the Law of Sines, and 2 1/2 pages later you have a symmetrical expression for one side. "Do not try this at home." Edited March 15, 2013 by bonanova Comment on proof Quote Link to comment Share on other sites More sharing options...

0 Debasis Posted March 18, 2013 Report Share Posted March 18, 2013 ... this triangle is equilateral.(If my drawing was correct.) Correct. Good job. I wonder if there is a proof of this that is not overly complex? Edit: Well, No. I just found the proof, and it's not beautiful for its simplicity. You start with the Law of Sines, and 2 1/2 pages later you have a symmetrical expression for one side. "Do not try this at home." oh i am so sorry .....i mistook it for the eulers line....my bad... Quote Link to comment Share on other sites More sharing options...

0 marksmanjay Posted March 24, 2013 Report Share Posted March 24, 2013 COMBINATION: 7129 Quote Link to comment Share on other sites More sharing options...

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## bonanova

Warm-up problem:Bisect the angles of a triangle.

Describe the point(s) where each bisector first intersects one of the others.

Now try this:Trisect the angles of a triangle.

Describe the points where each trisector first intersects one of the others.

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