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# Lesson 11.4: Circles and Arcs

## This lesson contains only examples and exercises related to circles and arcs.

An arc is a portion of a curve or circle. There are two basic braille symbols for arcs:

concave upward arc, dots one two four six, one
concave downward arc, dots one two four six, three

In print, the symbol for an arc appears over or on top of the letters that define the specified arc. Thus, you must follow the rules for a symbol that appears above the letters.

Step 1: The portion of the expression being modified must begin with the multipurpose indicator, dot five.
Step 2: The expression that is to be changed is brailled next.
Step 3: The directly over symbol, dots one two six, follows the expression.
Step 4: The symbol which appears directly over or directly under the expression is brailled.
Step 5: The termination indicator, dots one two four five six, indicates the position where the modification ends.

### Example 1

$\stackrel{^}{\mathrm{AB}}\phantom{\rule{.3em}{0ex}}\text{is a minor arc.}$
⠸⠩⠀⠐⠠⠁⠠⠃⠣⠫⠁⠻⠀⠸⠱⠀⠊⠎⠀⠁⠀⠍⠊⠝⠕⠗⠀⠁⠗⠉⠲

### Example 2

$\stackrel{^}{\mathrm{DEF}}\phantom{\rule{.3em}{0ex}}\text{is a major arc.}$
⠸⠩⠀⠐⠠⠙⠠⠑⠠⠋⠣⠫⠁⠻⠀⠸⠱⠀⠊⠎⠀⠁⠀⠍⠁⠚⠕⠗⠀⠁⠗⠉⠲

### Example 3

$m\stackrel{^}{\mathrm{AB}}={20}^{\circ }$
⠍⠐⠠⠁⠠⠃⠣⠫⠁⠻⠀⠊⠎⠀⠼⠆⠴⠘⠨⠡

### Example 4

$m\stackrel{^}{\mathrm{AB}}+m\stackrel{^}{\mathrm{CD}}$
⠍⠐⠠⠁⠠⠃⠣⠫⠁⠻⠬⠍⠐⠠⠉⠠⠙⠣⠫⠁⠻

### Example 5

$◯M$
⠫⠉⠀⠠⠍

### Example 6

$◯M\cong ◯P$
⠫⠉⠀⠠⠍⠀⠈⠱⠨⠅⠀⠫⠉⠀⠠⠏

### Example 7

$\stackrel{^}{\mathrm{AB}}\cong \stackrel{^}{\mathrm{CD}}$
⠐⠠⠁⠠⠃⠣⠫⠁⠻⠀⠈⠱⠨⠅⠀⠐⠠⠉⠠⠙⠣⠫⠁⠻

### Example 8

$\frac{m\stackrel{^}{\mathrm{AB}}}{360}$
⠹⠍⠐⠠⠁⠠⠃⠣⠫⠁⠻⠌⠒⠖⠴⠼