CIRCLES OBJECTIVE: Learn the basic terminology for circles and lines and segments associated with circles.

CIRCLES A circle is . . . . . THE SET OF ALL POINTS IN A PLANE THAT ARE EQUIDISTANT FROM A GIVEN POINT, CALLED THE CENTER. A circle is named by its center. P

CIRCLES Points inside the circle form the circle’s interior. Points outside the circle form the circle’s exterior. Exterior Interior

CIRCLES A radius is . . . A SEGMENT FROM THE CENTER TO A POINT ON THE EDGE OF THE CIRCLE. All radii are congruent. The length of the segment is also called the radius.

CIRCLES A diameter is . . . A LINE SEGMENT CONTAINING THE CENTER OF THE CIRCLE WITH ITS ENDPOINTS ON THE CIRCLE. The length of the segment is also called the diameter.

CIRCLES CONGRUENT CIRCLES HAVE THE SAME RADII

TWO OR MORE COPLANAR CIRCLES THAT HAVE THE SAME CONCENTRIC CIRCLES TWO OR MORE COPLANAR CIRCLES THAT HAVE THE SAME CENTER

CIRCLES An arc is . . . TWO POINTS ON A CIRCLE AND THE CONTINUOUS (UNBROKEN) PART OF THE CIRCLE BETWEEN THE POINTS.

CIRCLES A semicircle is . . . AN ARC WHOSE ENDPOINTS ARE THE ENDPOINTS OF A DIAMETER. A HALF-CIRCLE.

CIRCLES Minor arcs are . . . SMALLER THAN SEMICIRCLES. Major arcs are . . . LARGER THAN SEMICIRCLES.

CIRCLES A B C D

CIRCLES A B C D

CIRCLES A B C D

Arcs are measured in degrees. CIRCLES Arcs are measured in degrees. A full circle measures 3600 A B

CIRCLES A central angle is . . . AN ANGLE WITH ITS VERTEX AT THE CENTER OF A CIRCLE AND SIDES PASSING THROUGH THE ENDPOINTS OF AN ARC.

CIRCLES CENTRAL ANGLE

CIRCLES The measure of an arc is the same as the measure of its CENTRAL ANGLE.

ARC ADDITION POSTULATE CIRCLES ARC ADDITION POSTULATE The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

ARC ADDITION POSTULATE B C

CIRCLES A chord is . . . A LINE SEGMENT WHOSE ENDPOINTS LIE ON THE CIRCLE.

CIRCLES A tangent is . . . A LINE THAT INTERSECTS THE CIRCLE ONLY ONCE. The point where the tangent intersects the circle is the POINT OF TANGENCY

CIRCLES A secant is . . . A LINE THAT INTERSECTS A CIRCLE AT TWO POINTS.

CIRCLES INSCRIBED CIRCLES A circle is inscribed in a polygon if each side of the polygon is tangent to the circle.

CIRCUMSCRIBED CIRCLES A circle is circumscribed about a polygon if each vertex of the polygon lies on the circle.

CIRCLES COMMON TANGENTS

CIRCLES Common tangents are lines that are tangent to two circles. A common tangent that does not intersect the segment that joins the centers of the circles is a common external tangent. A common tangent that intersects the segment that joins the centers is a common internal tangent.