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Circles

Circles. What will we learn Parts of a circle including radius, diameter, arcs, angles How to find arc measures How to find angle measures. Parts of a Circle. A. C. B. D. Radius - segment from center pt to a point on the circle. Ex. AC, BC, DC are all radiuses. Parts of a Circle.

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Circles

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  1. Circles • What will we learn • Parts of a circle including radius, diameter, arcs, angles • How to find arc measures • How to find angle measures

  2. Parts of a Circle A C B D Radius - segment from center pt to a point on the circle. Ex. AC, BC, DC are all radiuses

  3. Parts of a Circle Chord - segment whose endpoints are on the circle. Ex. PR, PS, are chords Diameter - a chord that passes through the center point of a circle. Ex. PR is a diameter

  4. Parts of a Circle Arc- Part of a circle's edge Minor Arc- an arc that is less than 1800 - use two letters to label a minor arc. Ex. Major Arc - an arc that is more than 1800 - use three letters to label major arc. Ex.

  5. Parts of a Circle Central angle- an angle whose vertex is at the center of the circle. Ex. <APB Intercepted Arc – arc that is cut off by the sides of an angle. Ex. arc AB is the intercepted arc

  6. Parts of a Circle 1 Inscribed angle- an angle whose vertex is on the circle. Ex. <1 is an inscribed angle.

  7. A Put the answers to the following on your notesheet: Radius Diameter Major Arc Minor Arc Chord Central angle Inscribed Angle C L P T

  8. Central Angles 80 Central Angle = Intercepted Arc A B 1 In the picture at right arc AB = 80, so angle 1 = 80 because <1 is a central angle In the picture at right arc AC = 105, because its central angle is 105. 105 A 75 <1= 105 (vertical angles), <2=75 (forms a line with 105), <3 = 75 (forms a line with105). 105 C 75 2 105 3 1 B Therefore arc BD = 105, arc AB = 75, arc DC = 75 105 D

  9. Central Angles Central Angle = Intercepted Arc Put these on your notesheet 1 - Find x 2 - find x 30 L E A A 3 - find arc AB 4 - find angles 1, 2, 3 100 B C A x 110 x 1 D B 3 D 2 C 132 L A B 127 D

  10. Central Angles Central Angle = Intercepted Arc Put these on your notesheet 1 - Find x 2 - find x 30 110 30 30 E A L A X=110 because Central angle = intercepted arc X=30 because Central angle = intercepted arc so <ECA = 30, x is vertical to <ECA so x=30 C x 110 x D B

  11. Central Angles Central Angle = Intercepted Arc Put these on your notesheet 3 - find arc AB 53 53 127 100 48 80 132 4 - find angles 1, 2, 3 100 B Arc AD=127, arc AB and arc AD form a semicircle (180 degrees) 180-127=53 Or you could say the unlabeled angle next to 127 is 53 and then the arc is 53 A <1=100 b/c it is central to arch AB <2=80 b/c it forms a line with <1 (180-100 = 80) <3=48 b/c arc AD is 48 (180-132) 1 3 D 2 C 132 L A B 127 D

  12. Place these problems on your HALF SHEET OF PAPER

  13. Inscribed Angles Inscribed Angle = (Intercepted Arc)/2 Or Intercepted Arc = 2(Inscribed Angle) 70 98 A A B B 98 1 142 120 49 35 71 3 2 60 1 4 C C Above arc AB=98, so <1=98 (central angle=arc), <2=49 (inscribed angle = arc/2), <4=60 (inscribed angle = arc/2) <3=71 (180-49-60), arc AC=142 (arc=2(inscribed angle) Above arc AB = 70, so angle 1 = 35 because <1 is an inscribed angle

  14. Inscribed Angles Inscribed Angle = (Intercepted Arc)/2 Put these on your notesheet EX2 - Find arc AB, and x EX1 - Find x EX3 - Find arc AB and arc ATB A 4 - find angles 1, 2, 3 T 100 B A 80 56 145 A B x B D 3 1 2 132 L A x 1 B R C angle 1 = 90

  15. Inscribed Angles Inscribed Angle = (Intercepted Arc)/2 Put these on your notesheet EX2 - Find arc AB, and x EX1 - Find x 90 45 40 Arc AB=90 because an arc equals its central angle. Since angle x is inscribed and Intercepts arc AB, x = AB/2=45 A x = 40 because an inscribed angle equals half the intercepted arc 80 B x A x 1 B R C angle 1 = 90

  16. Inscribed Angles Inscribed Angle = (Intercepted Arc)/2 EX3 - Find arc AB and arc ATB 290 56 50 36 28 70 <1=50because it is an inscribed angle and half arc AB <2=28 because it is an inscribed angle and half arc BD <3=36, Arc AL=72 because 360-100-50-132=72. <3 is inscribed so it is 72/2 4 - find angles 1, 2, 3 T 100 Arc ATB is a major arc (more than 180). Arc ATB=290 {because the arc is twice its inscribed angle of 145} AB=170, because AB and ATB make the whole circle so 360-290=70 B A 145 A B D 3 1 2 132 L

  17. Place these problems on your HALF SHEET OF PAPER

  18. THE END

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