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

In summary, the conversation discusses Euler's triangle formula and how to solve for the circumradius (R) and inradius (r) when only the distance (d) between the incenter and circumcenter is known. The conclusion is that it is not possible to solve for both R and r with only the given information.
  • #1
mathius1
2
0
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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  • #2
You don't. You're not going to get two values out of one. (Think of an equilateral triangle of arbitrary size for instance.)
 
  • #3
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
 

1. What is Euler's triangle formula?

Euler's triangle formula, also known as Euler's polygon division formula, is a mathematical formula that relates the number of sides, vertices, and edges of a polygon. It states that the sum of the number of sides and vertices of a polygon is equal to the number of edges plus 2.

2. Who discovered Euler's triangle formula?

Euler's triangle formula was discovered by the famous mathematician Leonhard Euler in the 18th century. He was a Swiss mathematician and physicist who greatly contributed to the fields of mathematics and physics.

3. How is Euler's triangle formula used in geometry?

Euler's triangle formula is used in geometry to determine the number of sides, vertices, and edges of a polygon. It is particularly useful when working with complex polygons, as it provides a quick and easy way to calculate their properties.

4. Can Euler's triangle formula be applied to any polygon?

Yes, Euler's triangle formula can be applied to any polygon, regardless of its shape or size. It is a universal formula that works for all types of polygons, from simple triangles to complex polygons with many sides.

5. What is the significance of Euler's triangle formula?

Euler's triangle formula is significant because it provides a fundamental relationship between the properties of a polygon. It also has many practical applications in geometry, such as in the construction of polyhedrons and the calculation of their surface areas and volumes.

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