Circles

Points & Circle Relationships Inside the circle THE circle Outside the circle A C B E G F D

Parts of a Circle Center Radius Diameter Chord Is a diameter a chord? P A B R C D

Parts of a Circle Center: P Radius: PR Diameter: AB Chord: CD & AB Is a diameter a chord? YES P A B R C D

Construct a Regular Hexagon 1. With a compass – make a circle 2. DO NOT CHANGE compass measure

Construct a Regular Hexagon 3. Place point of compass on the circle

Construct a Regular Hexagon 4. Make an arc to the left and right side of the compass on the circle

Construct a Regular Hexagon 5. Move compass to arcs and repeat 4 & 5 until you have 6 marks

Construct a Regular Hexagon 6. Connect the consecutive marks

Major & Minor Arcs An Arc is part of a circle. Minor Arc is less than half Major Arc is more than half Identify the Minor Arcs and The Major Arcs… A C B E

Major & Minor Arcs Identify the Minor Arcs and The Major Arcs… Minor Arcs: AB, BC, AC Major Arcs: ABC, BCA, BAC A C B   E

Semicircles An arc that is exactly half the circle. D F E

Measure of Arc Arcs are measured in two ways Degrees Length

Arc Measure: Degrees The arc measure corresponds the the central angle. What is the mAB? A C B 120  95   P

Arc Measure: Degrees What is the mAB? A C B 120  95   P

Arc Measure: Degrees What is the mAB? 120 A C B 95   P

Arc Measure: Degrees What is the mAB? 120 What is the mBC? A C B 120  95    P

Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 A C B 120  95    P

Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? A C B 120  95     P

Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? 145 A C B 120  95     P

Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? 145 What is the mACB? A C B 120  95      P

Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? 145 What is the mACB? 240 A C B 120  95      P

Arc Measure: Length The length is part of the circumference… so you would have to know the radius. A C B 120  95  P

Arc Measure: Length The length is part of the circumference… so you would have to know the radius. And the formula Length = 2r A C B 120  95  5cm degree    P

Arc Measure: Length Length = 2r AB = A C B 120  95  5cm degree     P

Arc Measure: Length Length = 2r AB = 25(120/360) A C B 120  95  5cm degree     P

Arc Measure: Length Length = 2r AB = 25(120/360) = cm A C B 120  95  5cm degree     P

Arc Measure: Length Length = 2r AC = A C B 120  95  5cm degree     P

Arc Measure: Length Length = 2r AC = 25(145/360) A C B 120  95  5cm degree     P

Arc Measure: Length Length = 2r AC = 25(145/360) = cm A C B 120  95  5cm degree     P

Chords and Arcs Theorem What would you think if 2 chords of a circle had equal length? A CD B P

Chords and Arcs Theorem What would you think if 2 chords of a circle had equal length? A CD B P AC  BD ? 

Chords and Arcs Theorem What would you think if 2 chords of a circle had equal length? A CD B P AC  BD ? Prove it! 

Chords and Arcs Theorem Draw lines to each point What do you know about the dotted lines? A CD B P

Chords and Arcs Theorem AP  BP (radii of the same O are  CP  DP A CD B P

Chords and Arcs Theorem AP  BP (radii of the same O are  CP  DP A CD B P What do you know about the triangles?

Chords and Arcs Theorem The  ‘s are  by SSS A CD B P

Chords and Arcs Theorem The  ‘s are  by SSS A CD B P So where does this lead…

Chords and Arcs Theorem What do you know about angles 1 & 2? A CD B P 12

Chords and Arcs Theorem What do you know about angles 1 & 2? A CD B P 12 <1  <2 by CPCTC

Chords and Arcs Theorem So the Central angles are  And the arcs formed are  A CD B P