 # Mr. Burke's Geometry Class Page

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This page contains notes on all the topics which we have covered so far. You are responsible for all this material.

## Circles

### Parts of a Circle

Center: The point in the middle of the circle gives the circle its name. (Ex. Circle P has point P in the center.) Every point on the circle is an equal distance away from the center.

Diameter: A line segment going from one point of the circle to another point that passes through the center of the circle. All diameters in a given circle are congruent (the same size). The diameter is twice the size of the radius.

Raidus: A line segment going from the center of the center to a point on the circle. All radii in a given circle are congruent (the same size). The radius is half the size of the diameter.

Chord: A line segment going from one point of the circle to another point that passes. It does not have to pass through the center. The diameter is a chord that passes through the center of a circle.

Chords vary in length. They are NOT necessarily congruent. The closer a chord is to the center of the circle, the longer the chord will be. The diameter is the longest chord in a circle.

Arc: An arc is a curved line that is a part of the circle, measured from one point on the circle to another point on the circle. If an arc covers less than 180o, or less than half the circle, it is a minor arc. If an arc covers more than 180o, or more than half the circle, it is a major arc. Major arcs must have at least three letters in their names.

A semicircle is an arc which covers half of the circle, 180o.

### Circumference and the Length of Arcs

The circumference of a circle is the distance around the circle.

The ratio of the circumference to the length of the diameter is pi. We can sometimes use 3.14 as an approximation for pi. Use the pi key on your calculator for more accurate results.

To find the length of an arc of a circle, you need to know the size of the central angle that intercepts that arc. Divide the size of the angle by 360 and multiply that fraction by the circumference to find the length of the arc.

### Central Angles and Inscribed Angles

This is the next topic we will cover.