Proving a Right-Angled Triangle in a Rectangular Hyperbola | Homework Question

AI Thread Summary
A triangle inscribed in a rectangular hyperbola has a tangent at one vertex that is perpendicular to the opposite side, leading to the conclusion that the triangle is right-angled. Participants in the discussion express difficulty in visualizing the problem and request assistance with drawing a valid figure. One user suggests considering both halves of the hyperbola for clarity. A helpful figure is shared, prompting inquiries about the software used for its creation. The discussion emphasizes the importance of visual aids in solving geometric problems.
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Homework Statement


A triangle is inscribed in a rectangular hyperbola such that the tangent at one of the vertices is perpendicular to the opposite side. Prove that the triangle is right angled.


Homework Equations





The Attempt at a Solution



I am unable to draw a valid figure for this question. How can a tangent at vertex be perpendicular to the opposite side?
Can anyone upload a figure for this?
Thanks
 
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Have you tried drawing it with BOTH halves of the rect hyp? Can you show us what you have done in trying?
 
a is perpendicular to ED

EDF is right angled.


[PLAIN]http://img228.imageshack.us/img228/4846/69374949.jpg
 
Last edited by a moderator:
Thanks Quinzio. That helped.
Can you tell me which software did you use to draw this figure?
 
Abdul Quadeer said:
Thanks Quinzio. That helped.
Can you tell me which software did you use to draw this figure?

http://www.geogebra.org/cms/en
 

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