Math 12V Chapter 4 - Circle Geometry

 

Circle Properties

 

Section 4.1

1. All chords that are the same distance from the center of a circle have the same length.  Another way of writing this is, “All chords equidistant from the center of a circle are congruent.”

 

2. (Converse of Property # 1)  All chords that are the same length are the same distance from the center of the circle.

 

3. A line that is perpendicular to a chord of a circle and passes through the center of the circle bisects the chord.

 

4. (Converse of Property #3)  A line that is perpendicular to a chord of a circle and bisects the chord passes through the center of the circle.

 

Section 4.3

5. The measure of an arc is equal to the measure of the central angle subtended by the arc. 

(Note – a central angle is an angle with its vertex in the center of a circle.)

 

6. The measure of an inscribed angle is half the measure of the central angle subtended by the same arc. 

(Note – an inscribed angle is an angle with its vertex on the circumference of a circle.)

 

7.  All inscribed angles subtended by the same arc are equal.

 

8.  The measure of An angle inscribed in a semi-circle is always 90°.

 

Parallel and Perpendicular Slopes

 

Section 4.2