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Skills #2

Skills #2. 1. What symbol is used to name circle M? 2. The distance from the center to a point on a circle is __________. 3. The distance across a circle through the center is a ___________. 4. A chord is a segment whose _________ are on the circle.

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Skills #2

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  1. Skills #2 1. What symbol is used to name circle M? 2. The distance from the center to a point on a circle is __________. 3. The distance across a circle through the center is a ___________. 4. A chord is a segment whose _________ are on the circle. 5. A secant is a line that intersects at circle in _______ points. 6. A tangent is a line that intersects a circle at exactly ________ points. 7. The point where a tangent intersects a circle is a _____________. 8. A tangent is ___________ to a radius of the circle. 9. If 2 tangent lines originate at the same external point, the tangents are ______________. 10. A common internal tangent intersects the segment between the ________________ of a circle.

  2. Table of Contents 39. Section 10.2 Arcs and Chords

  3. 10.2 Arcs and chords Essential Question – How are the angles made by arcs and chords related?

  4. Central angle • Central angle- angle whose vertex is the center of a circle A ACB is a central angle C B

  5. Arcs • Arc- a piece of the outline of a circle. Named with 2 or 3 letters Measured in degrees B ( BP P

  6. Major and minor arcs • Minor arc- part of the outline of a circle that measures less than 180o (named by 2 letters). • Major arc- part of the outline of a circle that measures between 180o and 360o. (needs three letters to name) ( AC ( ABC http://www.mathopenref.com/arcminormajor.html

  7. Arc measures • Measure of a minor arc- measure of its central angle • Measure of a major arc- 360o minus measure of minor arc

  8. Ex: find the arc measures ( E m AB= m BC= m AEC= m BCA= 50o ( 130o ( A 180o 180o ( D 180o+130o = 310o 50o 130o C OR 360o- 50o = 310o B

  9. Arc addition • The measure of an arc formed by two adjacent arcs is the sum of the measures of those arcs. B A ( ( ( C m ABC = m AB+ m BC

  10. Congruent arcs • Congruent arcs- 2 arcs with the same measure • MUST be from the same circle OR  circles!!!

  11. Example ( m AB=30o A ( m DC=30o E 30o B D ( ( 30o AB @ DC C

  12. Example ( m BD= 45o A ( m AE= 45o B ( ( BD @ AE The arcs are the same measure; so, why aren’t they ? 45o C D E The 2 circles are NOT  !

  13. Congruent minor arcs • In the same circle (or in @ circles), 2 minor arcs are @ iff their corresponding chords are @. A ( ( AB @ BC iff AB@ BC B C

  14. ( Ex: find m BC B 3x+11 ( ( BD @ BC. 3x+11=2x+47 x=36 2x+47 2(36)+47 72+47 A 119o D C

  15. Diameters and chords • If a diameter of a circle is  to a chord, then the diameter bisects the chord and its arc. If EG is  to DF, then DC @ CF and DG @ GF ( ( E C D F G

  16. Congruent chords D C • In the same circle (or in  circles), 2 chords are  iff they are equidistant from the center. DE @ CB iff AG @ AF G F A E B

  17. Ex: find CG. CF @ CG B 6 72=CF2+62 G 49=CF2+36 6 A 13=CF2 CF = C  CG = D 7 6 F 6 E

  18. Assignment Pg. 607: 13-37 odd, 45, 47

  19. Assessment

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