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Chapter 9: Q16. (page 331)

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.

Short Answer

Expert verified

The centres of all circles passing through Aand B lie on a straight line.

Step by step solution

01

Step 1. Given information. 

Circles passes through two points A and B.

02

Step 2. Concept used.

Co-linear centers.

03

Step 3. Find value.

The points of centres of circles are co-linear, which are passing through the two intersection points, namely A and B.

Therefore, the centres of all the circles passing through A and B lie on a straight line.

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Most popular questions from this chapter

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).

Use a compass to draw a large ⊙o.Draw a central ∠AOB..

a. draw three other points P,Qand R that are on ⊙obut not on AB⏜.

then draw ∠APB,∠AQB and ∠ARB.

b. Use a protractor to find m∠AOB,m∠APB,m∠AQB and m∠ARB.

c. What is the relationship between m∠APB,m∠AQB and m∠ARB?

What is the relationship between m∠AOBand m∠APB?

For each exercise draw a circle and inscribe the polygon in the circle.

e. An acute isosceles triangle.

Given PA¯and PB¯ are tangents to ⊙o.

Use the diagram at the right to explain how the corollary on page 333

follows from Theorem9-1.

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

d. m∠AOB=120°
See all solutions

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