Geometry – Arcs, Central Angles, and Chords An arc is part of a circle. There are three types you need to understand: P Semicircle – exactly half of a circle 180° X BA

Geometry – Arcs, Central Angles, and Chords An arc is part of a circle. There are three types you need to understand: P P D C Minor arc – less than a semicircle ( < 180° ) Semicircle – exactly half of a circle 180° X BA

Geometry – Arcs, Central Angles, and Chords An arc is part of a circle. There are three types you need to understand: P P D C Minor arc – less than a semicircle ( < 180° ) Semicircle – exactly half of a circle 180° P Major arc – bigger than a semicircle ( > 180° ) X BA A B E

Geometry – Arcs, Central Angles, and Chords An arc is part of a circle. There are three types you need to understand: P P D C Minor arc – less than a semicircle ( < 180° ) Semicircle – exactly half of a circle 180° P Major arc – bigger than a semicircle ( > 180° ) X BA A B E The symbol for an arc ( ) is placed above the letters naming the arc

Geometry – Arcs, Central Angles, and Chords An arc is part of a circle. There are three types you need to understand: P P D C Minor arc – less than a semicircle ( < 180° ) Semicircle – exactly half of a circle 180° P Major arc – bigger than a semicircle ( > 180° ) X BA A B E The symbol for an arc ( ) is placed above the letters naming the arc AXB You need 3 letters to name a semicircle

Geometry – Arcs, Central Angles, and Chords An arc is part of a circle. There are three types you need to understand: P P D C Minor arc – less than a semicircle ( < 180° ) - Use the ray endpoints to name a minor arc Semicircle – exactly half of a circle 180° P Major arc – bigger than a semicircle ( > 180° ) X BA A B E The symbol for an arc ( ) is placed above the letters naming the arc AXB You need 3 letters to name a semicircle CD

Geometry – Arcs, Central Angles, and Chords An arc is part of a circle. There are three types you need to understand: P P D C Minor arc – less than a semicircle ( < 180° ) - Use the ray endpoints to name a minor arc Semicircle – exactly half of a circle 180° P Major arc – bigger than a semicircle ( > 180° ) - Use the ray endpoints and a point in between to name a major arc X BA A B E The symbol for an arc ( ) is placed above the letters naming the arc AXB You need 3 letters to name a semicircle CD BEA

Geometry – Arcs, Central Angles, and Chords A central angle is an angle whose vertex is at the center of a circle: P D C

Geometry – Arcs, Central Angles, and Chords A central angle is an angle whose vertex is at the center of a circle: P D C - This central angle creates an arc that is equal to the measure of the central angle. CD

Geometry – Arcs, Central Angles, and Chords A central angle is an angle whose vertex is at the center of a circle: P D C -This central angle creates an arc that is equal to the measure of the central angle CD The reverse is also true, if arc CD = 50°, central angle DPC = 50°

Geometry – Arcs, Central Angles, and Chords P D C Chord DC separates circle P into two arcs, minor arc DC, and major arc DYC. Y

Geometry – Arcs, Central Angles, and Chords P D C Theorem : if two chords of a circle have the same length, their intercepted arcs have the same measure. A B

Geometry – Arcs, Central Angles, and Chords P D C Theorem : if two chords of a circle have the same length, their intercepted arcs have the same measure. A B

Geometry – Arcs, Central Angles, and Chords P D C Theorem : if two chords of a circle have the same length, their intercepted arcs have the same measure. A B - The reverse is then also true, if intercepted arcs have the same measure, their chord have the same length.

Geometry – Arcs, Central Angles, and Chords P D C Theorem : if two chords of a circle have the same length, their intercepted arcs have the same measure. A B - The reverse is then also true, if intercepted arcs have the same measure, their chord have the same length. EXAMPLE : CD = AB and the measure of arc AB = 86°. What is the measure of arc CD ?

Geometry – Arcs, Central Angles, and Chords P D C Theorem : if two chords of a circle have the same length, their intercepted arcs have the same measure. A B - The reverse is then also true, if intercepted arcs have the same measure, their chord have the same length. EXAMPLE : CD = AB and the measure of arc AB = 86°. What is the measure of arc CD ?

Geometry – Arcs, Central Angles, and Chords P D C Theorem : chords that are equidistant from the center have equal measure A B X Y

Geometry – Arcs, Central Angles, and Chords P D C Theorem : chords that are equidistant from the center have equal measure A B X Y EXAMPLE : XP = YP and the measure of AB = 30. What is the measure of CD ?

Geometry – Arcs, Central Angles, and Chords P D C Theorem : chords that are equidistant from the center have equal measure A B X Y EXAMPLE : XP = YP and the measure of AB = 30. What is the measure of CD ?

Geometry – Arcs, Central Angles, and Chords P Theorem : If a diameter or radius is perpendicular to a chord, it bisects that chord and its arc. A B Y X

Geometry – Arcs, Central Angles, and Chords P Theorem : If a diameter or radius is perpendicular to a chord, it bisects that chord and its arc. A B Y X EXAMPLE : PY is perpendicular to and bisects AB, arc AB = 100°. What is the measure of arc YB ?

Geometry – Arcs, Central Angles, and Chords P Theorem : If a diameter or radius is perpendicular to a chord, it bisects that chord and its arc. A B Y X EXAMPLE : PY is perpendicular to and bisects AB, arc AB = 100°. What is the measure of arc YB ?