Learning About Circles

Circle n An infinite set of coplanar points that are an equal distance from a given point. O M M

Center n The point at the middle of the circle. n point M M

Radius n A segment whose endpoints are the center of a circle and a point on the circle. n A MA M

Chord n A segment whose endpoints are points on a circle. n A n B AB M

Diameter n A chord that contains the center of a circle. n A n B n n T AT M In O M

Circumference n The distance around a circle. C = 2  r M

Area n Number of square units contained in the interior of a circle. n n n n A =  r 2

Central Angle n An angle whose vertex is the center of a circle. n n A n B n n / AMB M

Arc n A continuous portion of the circle.

Minor Arc n An arc that is less than half of a circle. 0 O < x O < 180 O n A n B n n C AB (

Semicircle Semicircle n An arc whose measure is 180 O, exactly half of a circle. n n A B n T M AT when AT contains M M (

Major Arc Major Arc n An arc whose measure is more than half and less than one whole circle. 180 O < x O < 360 O n A n B n n C BAC (

Adjacent Arcs n Two arcs that share exactly one point. n A n B n C CA & AB ( (

Congruent Circles n Circles that have congruent radii. (circumferences, areas…)

Congruent Arcs n Two arcs in the same circle or congruent circles that have the same measure. n n B n C CA  AB ( ( A

Interior of the Circle n An infinite set of points inside the circle including the center. n n H I M K O M

Exterior of the Circle n All coplanar points that are outside a circle. R S T V P

Secant n A line that intersects a circle in exactly two points. n A n B n n C AB

Tangent n A coplanar line that intersects a circle in exactly one point. n A n B n D n C DB

Point of Tangency n The point in which a tangent intersects the circle. n A n B n D n C point B

Tangent Segments n Segment whose endpoints are a point on the tangent line and the point of tangency. n A n B n E n C BE

Common Tangent A line or segment that is tangent to two coplanar circles.

4 Common Tangents

3 Common Tangents

2 Common Tangents

1 Common Tangent

0 Common Tangent

Arc of the Chord n An arc that has the same endpoints as a chord. n A n B n n C CA & CA (

Inscribed Angle n An angle whose vertex is on the circle and whose sides are chords of the circle. n A n B n C / ABC

Intercepted Arc n An arc whose endpoints are the non-vertex points of an inscribed angle that intersect the circle. n A n B n n C AC (

Inscribed Polygon n A polygon where each of its vertices lies on a circle. n A n B n C n D quadrilateral ABDC

Circumscribed Polygon n A polygon with ALL sides tangent to a circle. n A n B n D n n F C pentagon ADCFB

Secant Segment n A segment on a secant from the exterior of a circle to a point on the circle so that it contains the chord. n B n C n A n AB

External Secant Segment n Part of secant segment that is in the exterior of the circle. n A n B n D n C BD

Arc Length n The length of the arc; part of the circumference proportional to the central angle. n A n B n m AB = x 360 O Circ. (

Arc Bisector n Any line, ray or segment that contains the midpoint of an arc. n A n B n C CA  AB ( (

Concentric Circles n Coplanar circles that have the same center.

Similar Circles n All circles are similar.

Space The set of all points. n

Sphere n An infinite set of points in space that are an equal distance from a given point.