Chapter 9.4, Problem 3CE

a.

To determine

To write: Theorem that justifies the given statement.

Explanation of Solution

Given information: $LK=8$

  $OE\perp LK$

As perpendicular from center to the chord bisects the chord,

  $LK=2LE$

Put $LE=4$

So,

  $LK=2\left(4\right)=8$

b.

To determine

To write: Theorem that justifies the given statement.

Explanation of Solution

Given information: $OE=3$

  

  $LK=GH=8$

As equal chords are at equidistant from the center,

  $OE=OF=3$

c.

To determine

To write: Theorem that justifies the given statement.

Explanation of Solution

Given information: $\stackrel{⌢}{LK}\cong \stackrel{⌢}{GH}$

  

  $LK=GH$

If two chords are equal in measure then their corresponding minor arcs are also equal.

So,

  $\stackrel{⌢}{LK}=\stackrel{⌢}{GH}$

Also, equal arcs are congruent.

  $\stackrel{⌢}{LK}=\stackrel{⌢}{GH}$