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

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Homework Help Overview

The problem involves a triangle inscribed in a rectangular hyperbola, with a specific condition regarding the tangent at one vertex being perpendicular to the opposite side. The goal is to prove that this triangle is right-angled.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses difficulty in visualizing the problem and questions how a tangent can be perpendicular to the opposite side. Some participants suggest drawing the figure using both halves of the hyperbola and inquire about the original poster's attempts.

Discussion Status

Participants are actively engaging in the discussion, with some providing helpful insights and suggestions for visual representation. There is no explicit consensus yet, but the conversation is moving towards clarifying the geometric relationships involved.

Contextual Notes

The original poster has requested a figure to aid understanding, indicating a potential gap in visualizing the problem setup. There is also mention of software used for drawing, which may suggest a reliance on visual tools for problem-solving.

zorro
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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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