Questions tagged [soddy-circles]

For questions regarding the definition, properties and applications of Soddy circles, the kissing circles in Descartes' theorem.

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Soddy Line in Slope Intercept Form

Given three coordinates of a triangle, is there a simple technique for representing that triangle's Soddy Line in slope intercept form? Edit: One of the points on the line (incenter), is super ...
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63 views

Another approach to Soddy circles formula

I am trying to prove a version of Descartes' theorem in an elementary way. Given three mutually tangent circles (no one is inside the others) with centres $A,B,C$ and radii $a, b, c$ respectively, I ...
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Need help with a problem regarding Descartes' theorem

I'm working on a general Apollonian gasket (i.e., with no particular symmetry). One example might be to populate a Steiner chain with Apollonian circles. I programmed a recursive Descartes' theorem ...
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I want to write an algorithm for two circles intersection and touching cases . How can I do it with a quadtratic equation? [duplicate]

Given that two circles with coordinates (x1, y1) and (x2, y2) and radius r1 and r2 respectively . I need to find an equation , which can be used in code to to find the coordinates and the presence of ...
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38 views

Geomentry and related to Circles

Two concentric circles are given,with two points initial at some point parallel to each other,v1 is given which is angle of movement of the point in circle A,v2 is given which is angle of movement of ...
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1k views

problem solving with regards to circle [closed]

a stadium is shaped, where its left and right ends are circular arcs both with center at C. what is the length of the stadium 50m from one of the straight sides? [here's the figure for the question][...
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1answer
866 views

Proving that a circle will contain n lattice points?

A lattice point is a point $(x, y)$ in the plane, both of whose coordinates are integers.It is easy to see that every lattice point can be surrounded by a small circle which excludes all other lattice ...
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2answers
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What is the name of the circle that is tangent to three mutually-tangent circles centered at the vertices of a triangle?

I want some information about the little 'tangent circle', but I don't have its name to search for it in the internet. What is it called?
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834 views

Circle tangent to three tangent circles (without the Soddy/Descartes formula)

We have three circles tangent to each other with radii $1$, $2$, and $3$. Another circle is tangent to the other circles; find the radius of that circle using elementary geometry, without the Soddy ...
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1answer
416 views

Center of Soddy Circle

Given two points inside the unit circle, $(x_1, y_1)$ and $(x_2, y_2)$, let $C_1$ and $C_2$ be the circles with centers at those points, respectively, which are internally tangent to the unit circle. ...
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180 views

A question about the Soddy incircle

Let $a$, $b$, and $c$ be the centers of three circles that are mutually tangent, and let $B_r(s)$ be the Soddy incircle, tangent to all three. My question is whether one can disprove the statement: ...