[Math] Hyperbolic Ideal Triangle

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I have everything pretty much figured out everything but I need help proving the unique point formed by the three perpendiculars in the picture

Best Answer

  1. In the hyperbolic plane all the "great triangles or ideal triangles" (whose angles are all zeros) are congruent. So if you can prove something in the case of one of them will be true for all of them.

  2. Consider the Klein model and take a special great triangle: one of the great triangles that look equilateral in the Euclidean eye. The perpendicular (Euclidean) bisectors dropped from the vertices to the opposite sides will meet in the center of the Klein circle.

  3. If a hyperbolic line goes through the Klein center and is perpendicular to another hyperbolic line in the Euclidean sense, will be perpendicular to that line in the hyperbolic sense as well.

  4. Every great triangle will have this property. (Not that they meet at "the centre" : ) but the perpendiculats mentioned above have to meet.)
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