14-4 Arcs of Circles

14-4 Arcs of Circles Learn vocabulary; Central Angle, Minor arc, Major arc, Semi circle. Learn definition of degree measure.

A central angle of a circle is an angle whose vertex is the center of the circle. A P B

Let C be a circle with center P, and let A and B be points which lie on C but are not the end points of the same diameter. • Then the minor arc AB is the union A, B, and all points of C that lie in the interior of <APB. A C P B

Let C be a circle with center P, and let A and B be points which lie on C but are not the end points of the same diameter. • Then the Major arc AXB is the union A, B, and all points of C that lie in the exterior of <APB. A C P B x

What is the intersection of major and minor arc AB and AXB? What is the Union of the major and minor arc AB and AXB

Let C be a circle, and let A and B be the end points of a diameter. • A semicircle AXB is the union of A, B, and the points of C that lie in a given half-plane with AB as edge. C x A B P

(1) The degree measure of a minor arc is the measure of the corresponding central angle. A X r B mAXB = r.

(2) The degree measure of a semicircle is 180. X B A mAXB = 180.

(3) the degree measure of a major arc is equal to 360 minus the measure of the corresponding minor arc. A r X B mAXB = 360-r

Theorem 14-15 The Arc Addition Theorem • If B is a point of AC • then mABC = mAB + mBC. A B C

Pg. 469(1,2,4-6) Pg. 465(5)

14-4 Arcs of Circles