# Circles and Euler spiral (repost from general math)

• Mario

#### Mario

Hi,
i have this problem..., giving two circle (example radius 1 = 500 units, radius 2 = 200 units, distance between centers = 275.73 units) find Euler Spiral (aka Cornu spiral, aka Clothoid https://en.wikipedia.org/wiki/Euler_spiral) tangent giving circle (unknown tangent points).
For this problem are two mirrored Euler spiral as solution with length = 450 units.
Problem so simply to explain but not so simply to find solution...
Many thanks for help... Hello again, Mario, and again, too

Well, we are making progress. There is a problem statement and the link gives a bunch of equations. So we can claim 1 and 2 below are filled in.
All we have to do now is make a start with 3 !

## The Attempt at a Solution

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Oh, and: don't erase the template (or was your thread moved here by a moderator?)

For a start: how did you find the 275.73 ?

## Homework Statement

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known data:
center of circle 1 (xO1,yO1) and radius of circle = R1
center of circle 2 (xO2,yO2) and radius of circle = R2

unknown data:
lenght of spiral (magenta and blue) L=?
tangent point of spiral on circle 1 (xA, yA) = ?
tangent point of spiral on circle 2 (xB, yB) = ?

## Homework Equations

Particular declination of problem are resolved with below equation, but in this resolution know data are:
R1, R2, L, xA=zero, yA=zero, xO1=zero, yO1=R1, line(O1-A) is orthogonal to x axes
calculated data are:
xO2, yO2, xB, yB    (complete document at this link http://www.mygeodesy.id.au/documents/Horizontal Curves.pdf prof. R.E.Deakin)

## The Attempt at a Solution

A iterative solution is using the above equations and change L to find desidered distance of two circle...
but Analitical solution is possible ?
many thanks

P.S. move post here, if I understood well, it was a hint