Chapter 9, Problem 15CR

z

To determine

To state: the theorem that allows to deduction $XE=XF$ .

Answer to Problem 15CR

In same $\odot$ , $\cong$ chords are equally distant from the center.

Explanation of Solution

Given information:

Given statement,

If $\overline{AC}\cong \overline{DC}$

In $\odot X,marcAC=120$ .

Calculation:

Consider the following diagram:

.

In the referred diagram, $\overline{AC}\cong \overline{DC}$

Consider the theorem which says that, in same $\odot$ , $\cong$ chords are equally distant from the center.

Therefore, from the above triangle, it can be deducted that $XE=XF$ .