)Megrs said:
tiny-tim said:Hi Megrs@!
(have a pi: π and a degree: ° and try using the X2 tag just above the Reply box
You're almost there!
Stay with that triangle …
it has the shaded area inside it, so what's left?
)tiny-tim said:Hi Megrs!
(what happened to that π i gave you?
Yes, three sectors …
now, you know the radius and the angle of each sector, so the area is … ?
…tiny-tim said:so as a factor of r, the area of a sector is … ?
Megrs said:
Three mutually tangent circles are three circles that intersect each other at exactly one point, where each circle is tangent to the other two. This means that they share a common tangent line at the point of intersection.
The radii of three mutually tangent circles are related by a specific ratio known as the triple tangent ratio. This ratio is equal to the product of the three radii divided by the sum of the products of each pair of radii. In simpler terms, it can be written as (r1*r2*r3)/(r1*r2 + r2*r3 + r1*r3).
Three mutually tangent circles have various applications in mathematics, including in geometry, trigonometry, and complex analysis. They are also used in various engineering and design problems, such as finding the optimal size and position of three intersecting pipes or cables.
The centers of three mutually tangent circles can be found by drawing the common tangent lines between each pair of circles and finding the intersection point of these lines. This point will be the center of all three circles.
Yes, three mutually tangent circles can have different radii. However, the triple tangent ratio will still hold true and the radii will be related in a specific way. The radii can also be equal, which would result in three identical circles.