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If one circle is completely inside the other (< | |) then they have no bitangents, as a tangent line to the outer circle does not intersect the inner circle, or conversely a tangent line to the inner circle is a secant line to the outer circle. Finally, if the two circles are identical, any tangent to the circle is a common tangent and hence ...
All tangent circles to the given circles can be found by varying line . Positions of the centers Circles tangent to two circles. If is the center and the radius of the circle, that is tangent to the given circles at the points ,, then:
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 ...
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 ...
If the two given circles are tangent at a point, the Steiner chain becomes an infinite Pappus chain, which is often discussed in the context of the arbelos (shoemaker's knife), a geometric figure made from three circles. There is no general name for a sequence of circles tangent to two given circles that intersect at two points.
If the angle subtended by the chord at the centre is 90°, then ℓ = r √2, where ℓ is the length of the chord, and r is the radius of the circle. If two secants are inscribed in the circle as shown at right, then the measurement of angle A is equal to one half the difference of the measurements of the enclosed arcs (⌢ and ⌢).
The tangent lines must be equal in length for any point on the radical axis: | | = | |. If P, T 1, T 2 lie on a common tangent, then P is the midpoint of ¯.. In Euclidean geometry, the radical axis of two non-concentric circles is the set of points whose power with respect to the circles are equal.
The opposite is also true — every circle which is tangent to two other circles touches them at a pair of antihomologous points. Figure 5: Every circle which is tangent to two given circles touches them at a pair of antihomologous points. Let our two circles have centers O 1, O 2 (Figure 5). E is their external homothetic center.