Can You Solve Euler's Triangle Formula with Just the Distance (d)?

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SUMMARY

The discussion centers on Euler's triangle formula, specifically the relationship between the distance (d) from the incenter to the circumcenter of a triangle and the circumradius (R) and inradius (r). The formula d² = R(R - 2r) indicates that knowing only the distance (d) is insufficient to uniquely determine both R and r. Participants confirm that without additional information, such as the triangle's type or size, it is impossible to compute both values from a single distance measurement.

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  • Knowledge of circumradius (R) and inradius (r)
  • Basic algebra skills
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mathius1
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Hi all

I have a question concerning Euler's triangle formula, where the distance (d) between the incenter and circumcenter of a triangle is given as d2 = R(R-2r), with R being the circumradius and r the inradius. I suck at algebra and I need to know how to solve this if I only know the distance (d) and nothing else. How do I compute R and r from just the distance?

Many thanks
Nigel
 
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You don't. You're not going to get two values out of one. (Think of an equilateral triangle of arbitrary size for instance.)
 
Martin Rattigan said:
You don't. You're not going to get two values out of one. (Think of an equilateral triangle of arbitrary size for instance.)

Hi Martin

Thanks for the reply, I suspected that would be the case but wanted to make sure!

Cheers
Nigel
 

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