14-4 Arcs of Circles

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# 14-4 Arcs of Circles - PowerPoint PPT Presentation

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.

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### 14-4 Arcs of Circles

Learn vocabulary; Central Angle, Minor arc, Major arc, Semi circle. Learn definition of degree measure.

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

• 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.

(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