Chapter 9.1, Problem 4WE

a.

To determine

To explain: $QR=QS=QT$

Answer to Problem 4WE

  $QR=QS=QT$

Explanation of Solution

Given information:

Sphere is cut by a plane Z.

 

In sphere all points on surface are equidistant from the center when the plane cuts the sphere. Since all three given points; R, S, and T lie on the surface of the sphere, they are also equidistant from the point Q, which is the centre of the sphere.

Hence, $QR=QS=QT$ $\square$

b.

To determine

To explain: why the intersection of a plane and a sphere is a circle. 

Answer to Problem 4WE

Figure is a circle.

Explanation of Solution

Given information: 

Sphere is cut by a plane Z.

 

Since we know that the intersection of any plane passing through the centre of the sphere forms a great circle and a sphere is a three − dimensional symmetric version of a circle (with varying radius), then the figure so formed by the intersection of a plane and a sphere is always a circle.