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Chapter 9: Q13. (page 336)

Is there a theorem about spheres related to the theorem in Exercise 12? If so, state the theorem.

Short Answer

Expert verified

Two planes tangent to a sphere at the end points of diameter are parallel.

Step-by-step solution

Step by step solution

01

Step 1. Given information.

Theorem about spheres.

02

Step 2. Concept used.

The theorem that two lines tangent to a circle at the end points of diameter are parallel is also true for sphere.

03

Step 3. Theorem.

For sphere the theorem states that two planes tangent to a sphere at the end points of diameter are parallel.

Therefore, Yes. Theorem about spheres related to the theorem in Exercise 12.

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Most popular questions from this chapter

Given: Two tangents circles; EF炉 is a common external tangent;

GH炉 is the common internal tangent.

a. Discover and prove something interesting about point G.

b. Discover and prove something interesting about 鈭�EHF.

Draw two points A & B and several circles that pass through A and B. Locate the centers of these circles. On the basis of your experiment, complete the following statement:

The centers of all circles passing through A and B lie on ______.

Write an argument to support your statement.

For each exercise draw 鈯�O with radius 12. Then draw radii OA炉 and to OB炉 form an angle with the measure named. Find the length of AB炉.

a. m鈭�AOB=90掳

Plane Z passes through the center of sphere Q.

  1. Explain why QR=QS=QT.
  2. Explain why the intersection of the plane and the sphere is a circle. (The intersection of a sphere with any plane passing through the center of the sphere is called a great circle of the sphere).

Name a secant of the sphere and a chord of the sphere.
See all solutions

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