Internally Tangent A Large Sphere

The six spheres are internally tangent to a larger sphere whose center is the center of the hexagon. An eighth sphere is externally tangent to the six smaller spheres and internally tangent to the larger sphere. large sphere where they touch but do not overlap. Additionally, confirming the tangential relationships aids in understanding

Problem 4. Three circles of radius 1 are externally tangent to each other and internally tangent to a larger circle. What is the radius of the large circle? Problem 5. Two circles of radius 5 are externally tangent to each other and are internally tangent to a circle of radius 13 at points A and B, as shown in the diagram. Find AB. BA Problem 6.

The 8th sphere must be sitting atop of the spheres, which is the only possibility for it to be tangent to all the small spheres externally and the larger sphere internally. The ring of small spheres is symmetrical and the 8th sphere will be resting atop it with its center aligned with the diameter of the large sphere.

We are given center and radius of a sphere as cc1,c2,c3 and r respectively and a external point kk1,k2,k3,we have an other point pp1,p2,p3given in some linear parametric form such that kp is tangent to sphere. We have to find the variables of parametric forms of p. My approach

The four small spheres form a ring with each of the four spheres externally tangent to its two neighboring small spheres. A sixth intermediately sized sphere is internally tangent to the large sphere and externally tangent to each of the four small spheres. Its radius is m, where m and n are relatively prime positive integers. Find m n.

92begingroup There is also a large sphere tangent to the four smaller spheres, which are internally tangent to this large sphere how can this large sphere be drawn? 92endgroup - csn899. Commented Apr 11, 2024 at 757. 1 92begingroup The outer sphere to the original question is trivially just Spherecenter, 1 r. The other modification

The theorem does work again with one external tangent pair and two internal tangent pairs ma, mbmc, -mb ma, mc. Solution 4. This solution is by Martin Rebas. See the three circles as three spheres of equal size, but projected in 3d, so the biggest circle represents the sphere that is closest to the viewer, and so on.

Any four mutually tangent spheres determine six points of tangency. A pair of tangencies t_i,t_j is said to be opposite if the two spheres determining t_i are distinct from the two spheres determining t_j. The six tangencies are therefore grouped into three opposite pairs corresponding to the three ways of partitioning four spheres into two pairs. These three pairs of opposite tangencies are

The six spheres are internally tangent to a larger shepere whose center is the center of the hexagon. An eighth sphere is externally tangent to the six smaller spheres and internally tangent to the larger sphere. What is the radius of this eighth sphere? A. square root of 2 B. 32 C. 53 D. square root of 3 E. 2 Thanks in advance!