Chapter 9.4, Problem 1ST1

Solution

a.

To identify: two radii of the given circle with centre Q.

$\overline{QB}$ And $\overline{QC}$

Given:

The figure:

Explanation:

Consider the given figure:

Now, using the definition of radius, it can be said that the radii of the given circle are:

$\overline{QB}$ And $\overline{QC}$

b.

To identify: a diameter of the given circle with centre O.

  $\overline{BC}$

Given:

The figure:

Concept Used:

Definition:

Diameter: Any segment which passes through the centre O of the circle and whose end points lie on the circle is called diameter of the circle.

Explanation:

Consider the given figure:

Now, using the definition of diameter, it can be said that the diameter of the given circle is:

  $\overline{BC}$

C.

To identify: a chord and a secant of the given circle with centre O.

Chord: $\overline{AC}$

Secant: $\overleftrightarrow{AC}$

Given:

The figure:

Concept Used:

Definition:

Chord: Any segment whose end points lie on the circle is called chord of the circle.

Secant: It is a line which contains the chord.

Explanation:

Consider the given figure:

Now it can be observed that $\overline{AC}$ is a segment whose end points A and C lie on the circle. So by above definition, it is a chord.

Also, $\overleftrightarrow{AC}$ is a line which contains the chord $\overline{AC}$ , so by definition it is a secant.