Circles 3/30/09

Circle Definition A circle is the set of all points in a plane that are equidistant from a given point in the plane known as the center of the circle. How do we represent a circle

Parts of A Circle Radius A segment from the center of the circle to a point on the circle.

What can we say about all the radii of a circle? They are all equal! 8

Parts of a Circle CHORD Is a segment whose endpoints lie on a circle.

Parts of a Circle Diameter Is a chord that contains the center of a circle.

Diameter/Radius What do we know about the radius of a circle and its diameter? The diameter is TWICE the radius.

Parts of a Circle Arc Endpoints An unbroken part of a circle. Any two distinct points on a circle divide the circle into two arcs. Endpoints The two distinct points of the arcs

Parts of a Circle Semicircle An arc whose endpoints are endpoints of a diameter. Also known as a “half-circle”

Parts of a Circle Minor Arc Major Arc Is an arc that is shorter than a semicircle of that circle Major Arc Is an arc that is longer than a semicircle of that circle.

Parts of a Circle Central Angle It is an angle whose vertex is the center of the circle.

Degree Measures of Arcs The degree measure of a MINOR ARC is the measure of its central angle.

Degree Measures of Arcs The degree measure of a major arc is 360o minus the degree measure of its minor arc.

Degree Measures of Arcs

Degree Measures of Arcs The degree measure of a semicircle is 180o

Arc Length If r is the radius of a circle and M is the degree measure of an arc of the circle, then the length, L, of the arc is given by the following:

Class Work WS 9.1

Homework Page 570 11-19