You may be asked to calculate a missing value for part of a circle. These can take many different forms, but if we fully understand the parts of a circle, they are easy calculations.

**Strategy****:**

**All circle problems will be asking you to relate one part of a circle to another (for instance, diameter to circumference).****These problems can be solved 100% of the time by just plugging in to the proper, simple formula.****You must know these formulas. There’s no tricks or shortcuts here.**

There are a couple of basic formulas you should have memorized, but if not, they are in the reference section for the math section. A common mistake is confusing the two!

The **area** equals pi times the radius squared. The **circumference** equals two times pi times the radius, or pi times the diameter.

They also tell us in the reference:

**The number of degrees of arc in a circle is 360****The number of radians of arc in a circle is 2π**

So, 360 degrees = 2π radians.

**To convert from degrees to radians**, multiply the degrees by (fracpi{180}).

**To convert from radians to degrees**, multiply by (frac{180}{mathrmpi}) . Note the (pi) will always cancel to leave you with just a number.

An **arc** is the distance between two points on a circle. It can be expressed in degrees, radians, or units such as inches. Here, there is an arc between *A* and *B*, denoted as arc *AB*.

The degrees in the central angle (angle starting from the center of the circle) is equal to the degrees in the arc. So below, minor arc *AB* = 45° since the central angle is 45°.

A minor arc is less than a semicircle (180°) and a major arc is more than a semicircle. If they don’t specify, assume the minor arc.

There is a very important relationship between central angles, sector area and sector arc length. It is easy to understand when you think of eating a slice of pizza.

This concept gives us one of the most important equation for circles:

$$frac{central;angle}{360^circ}=frac{arc;length}{circumference}=frac{area;of;sector}{area;of;circle}$$

Or in terms of pizza:

$$frac{central;angle;of;slice}{360^circ}=frac{slice;crust}{total;crust}=frac{area;of;slice}{area;of;total;pizza}$$

Applying this concept to the above pizza, you can see that one slice of pizza will be 1/6 of the total area of the pizza. Additionally, the crust will be 1/6 of the total crust of the pizza. Finally, since the pizza has 360°, the central angle of the slice of of pizza will be 60°, because 1/6 * 360° is 60°.

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