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In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency : internal and external. Many problems and constructions in geometry are related to tangent circles; such problems often have real-life applications such as trilateration and maximizing the ...
Two different methods may be used to construct the external and internal tangent lines. External tangents Construction of the outer tangent. A new circle C 3 of radius r 1 − r 2 is drawn centered on O 1. Using the method above, two lines are drawn from O 2 that are tangent to this new circle.
For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the extended Euclidean plane. Monge's theorem states that the three such points given by the three pairs of ...
If the circles have the same center but different radii, both the external and internal coincide with the common center of the circles. This can be seen from the analytic formula, and is also the limit of the two homothetic centers as the centers of the two circles are varied until they coincide, holding the radii equal.
If , are tangent from different sides of (one in and one out), is the length of the interior common tangent. The converse of Casey's theorem is also true. [4] That is, if equality holds, the circles are tangent to a common circle.
By contrast, an internal tangency is one in which the two circles curve in the same way at their point of contact; the two circles lie on the same side of the tangent line, and one circle encloses the other. In this case, the distance between their centers equals the difference of their radii.
RB Derrick Henry, Baltimore Ravens. Henry's contract with the Ravens has a number of incentives he's already earned. He had incentives of $500,000 each when he hit 1,200 and 1,500 rush yards ...
Kissing circles. Given three mutually tangent circles (black), there are, in general, two possible answers (red) as to what radius a fourth tangent circle can have. In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this ...