Three Tangents to a Sphere

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Two lines, and , are tangent to a sphere at points and , respectively. Find the line that is tangent to the sphere and intersects the other two tangents.

[more]

Call the point of tangency and let the intersection of with and be and . Determine the set of all points .

[less]

Contributed by: Izidor Hafner (April 2017)
Open content licensed under CC BY-NC-SA


Snapshots


Details

If and are unit vectors parallel to and , a point lies on a plane that contains the line and forms equal angles with and . There are two such planes; one is parallel to , the other to . So all are in the intersections of these two planes with the sphere, that is, on two circles on the sphere. In this Demonstration we show one of them [1, p. 224].

Reference

[1] V. V. Prasolov and I. F. Sharygin, Problems in Stereometry (in Russian), Moscow: Nauka, 1989.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send