GRCA625

Chapter 9

Chapter 9.1

Chords and Arcs Objectives Circle- A circle is the set of all points in a plane that are and equal distant from a given point in the plane. This point is know as the center of the circle. Radius- A radius is a segment from the center of the circle to a point on the circle. Chord- A chord is a line segment whose end points land on the circle. Diameter- The diameter is twice the distance of the radius. It is a chord that contains the center of a circle. Arc - Is an unbroken part of a circle. It contains any points on a circle that divides the circle into two arcs. SemiCircle - Is what you may know better as a half-circle. Minor Arc - An arc that is smaller then a semicircle. A minor arc is named by its endpoints Major Arc - Is larger then a Semicircle ans is named by its two endpoints and another point on that arc. Interesting Thing about circles - [|Click Here] Degree Measure of an Arc - The degree measure of an minor arc is the measure of its central angle. The degree measure of an major arc is 360 - the degree of the minor arc. So if you want to know the major arc you take 360 - the minor arc. Arc Length - R = radius M = degree measure of an arc L = length of the ar L = M divided by 360(2 pi r)
 * 1) Define a circle and its associated parts.
 * 2) Define and use the degree measure of arcs.
 * 3) Define and use the length measure of arcs.
 * 4) Prove a theorem about chords and their intercepted arcs.



9.2

Objectives 1. Define tangents and secants. 2. Find relationship between tangents and radii of circle. 3. Understand the geometry of a radius perpendicular to a chord of a circle.

Secant – a line that intersects a circle at two points. Tangent – a line in the plane of a circle that intersects a circle at exactly one point. This point is known as a point of tangency. Tangent Theorem – If a line is tangent to a circle, then the line is perpendicular to a radius of a circle. Radius and Chord Theorem – A radius that is perpendicular to a chord of a circle bisects the chord. Converse of the Tangent Theorem – If a line is perpendicular to a radius of a circle at its endpoints to a circle. If this is true then the line is tangent to the circle.

The perpendicular bisectors of a chord pass through the center of a circle.

9.3

Objectives
 * 1) Define inscribed angle and intercepted arc.
 * 2) Develop and use the inscribed Angle Theorem.

Inscribed Angle – an angle that Inscribed Angle Theorem – The measure of and angle inscribed in a circle is equal to one half of the measure of the intercepted arc. Right Angle Corollary – If an inscribed angle intercepts the semicircle then the angle is right angle.

Arc Intercept Corollary – If two inscribed angles cross at the same arc, then the have the same angle measure. 9.4 All Photos with out links created by me.