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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

For Exercises 39 to 44, make drawings as needed.

Two tangent segments are drawn to sphere Q from external point E. Where A and B are the points of tangency on sphere Q, how are E A - and E B - related?

To determine

To find:

The relation of two tangent segments of a sphere, drawn from an external point.

Explanation

Approach:

A sphere is a three dimensional solid figure, which is made up of all points in the space, which lie at a common distance, called the radius, from a fixed point called the center of the sphere. A sphere is a 3 dimensional version of a circle. Similar to a circle, a sphere may have tangent and secant lines. In addition, the sphere may also have tangent planes.

1) A line which intersects a sphere in two distinct points is called the secant of a sphere.

2) A line which intersects a sphere in only one point is called the tangent to a sphere.

3) A tangent to a sphere is perpendicular to the radius at the point of contact.

4) A tangent plane is a plane which intersects sphere in only one point.

Calculation:

Two tangent segment EA¯ and EB¯ are drawn to sphere Q from point E, an external point.

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