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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

Three circles are shown. How many circles tangent to all three of the given circles can be drawn ?

Name a secant of the sphere and a chord of the sphere.

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.

d. m鈭�AOB=120掳

a. Given:WZ炉is a diameter of 鈯�o;OX炉鈭�ZY炉

Prove: WX铃�鈮�XY铃�.

(Hint: draw OY铃�.)

Draw a diagram similar to the one shown, but much larger. Carefully draw the perpendicular bisectors of AB炉 and BC炉.

  1. The perpendicular bisect in a point. Where does that point to be?
  2. Write an argument that justifies your answer to part (a).
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