Going Around in Circles!

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Presentation transcript:

Going Around in Circles! Chapter 10 – Honors Geometry

Parts of a Circle and their Definitions Set of all points in a plane that are a given distance from a given point in the plane. Center The given point referred to in the definition of the circle. A circle is named by its center! CENTER Given point Given distance RADIUS Radius The given distance referred to in the circle definition – the segment connecting the center to the circle – the distance from the center to the circle.

Parts of a Circle and their Definitions Concentric Circles Two or more coplanar circles with the same center

Parts of a Circle and their Definitions A point is inside (in the interior) a circle if its distance from the center is less than the radius. A point is on a circle if the distance from the center is equal to the radius. A point is outside (in the exterior) a circle if its distance from the center is more than the radius. POINT on a circle INTERIOR of a circle EXTERIOR of a circle

Parts of a Circle and their Definitions Chord A chord of a circle is a segment that connects any two points on the circle. A chord that passes through the center is called the DIAMETER of the circle

Parts of a Circle and their Definitions Circumference The perimeter of or distance around a circle is called the circumference of a circle. Check out about how the circumference of the earth was found http://video.google.com/videoplay?docid=8157409168878797983&q=circumference&hl=en

Parts of a Circle and their Definitions Area of a Circle

Parts of a Circle and their Definitions Enjoy the video! Circles Radius Diameter & Pi from Math Upgrade

Theorems for Circle Radii and Chords If a radius is perpendicular to a chord then it bisects the chord If a radius of a circle bisects a chord that is not a diameter, then it is perpendicular to that chord. The perpendicular bisector of a chord passes through the center of the circle.

Let’s try some problems! Circles! Let’s try some problems!

Theorems for Circle Congruent Chords If two chords of a circle are equidistant from the center, then they are congruent. If two chords of a circle are congruent, then they are equidistant from the center of the circle.