Interesting problem... I tried solving it through isosceles triangles, and I've proved it doesn't work on equilateral triangles. Can anyone give me some hints towards a geometric proof?
Can two angle bisectors of a triangle be perpendicular?
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geometry
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0I know it works, but I need a geometric proof that it is true. – 2010-11-02
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0If you're going to take the coordinate geometry route, draw a line intersecting both the horizontal and vertical axes. If you know the slope of the line, you know the angles it makes with the horizontal and vertical axes. Reflect the line along the horizontal and vertical axes, and find the intersection point of those two reflected lines. – 2010-11-02
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0(and if you actually tried out my suggestion, one look at the equations of those reflected lines will give you the logical conclusion, without having to solve for the intersection point) – 2010-11-02