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Theorems Of Circles

Theorems Of Circles. Chapter 10 Mr. Mills. Sum of Central Angles. The sum of the measures of the central agles of a circle with no interior points in common is 360 degrees. Draw circle p with radii PA, PB, PC. The sum of the measures of angles APB, BPC, CPA is 360 degrees. Congruent Arcs.

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Theorems Of Circles

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  1. Theorems Of Circles Chapter 10 Mr. Mills

  2. Sum of Central Angles • The sum of the measures of the central agles of a circle with no interior points in common is 360 degrees. • Draw circle p with radii PA, PB, PC. The sum of the measures of angles APB, BPC, CPA is 360 degrees.

  3. Congruent Arcs • In the same circle or congruent circles, two arcs are congruent if and only if their corresponding central angles are congruent. • Draw Circle P with radii PA and PB. Draw chord AB. • Draw an angle CPD that is congruent to central angle APB.

  4. Congruent arcs • Draw circle E with congruent angles RED and SET. • What do you know about Minor arcs RD and ST ? • If arc ST has a length of 27 inches, what is the length of arc RD?

  5. Congruent Minor Arcs • In a circle or congruent circles, two minor arcs are congruent, if and only if their corresponding chords are congruent. • Draw circle P with chord AB and Chord CD. So that the two chords are congruent.

  6. Congruent Minor Arcs • Draw circle E with congruent chords AB and CD. • What do we know about arcs AB and CD? • If the measure of arc AB is 56 degrees, what is the measure of arc CD?

  7. Diameter or Radius • In a circle, if a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc. • Draw circle P with chord AB and radius CP that is perpendicular to chord AB.

  8. Diameter and Radius • Draw circle E with radius EZ perpendicular to chord AB. Label the intersection of the chord and radius as point M. • IF AB has length 10,Find AM and BM • If AB has length 10 and the radius is 6 find EM, the distance form the center.

  9. You do the Math M X RM = 8 XP = 3 Find MP R P

  10. You do the Math M X RX = 12 XP = 5 Find MP Find XM Find RM R P

  11. You do the Math M X If RM is congruent to ST , XP is 8, and XM is 6. Find PS Find ST Find Pl R P L S T

  12. Page 543 #7 Tell why the measure of angle CAM is 28 degrees. Hint: Think SSS.

  13. Page 543 # 8 • Explain how to show that the measure of arc ES is 100 degrees. Hint: The sum of interior angles of a triangle is 180 degrees.

  14. Page 543 • # 9 • Explain how to show the length of SC is 21 units.

  15. Inscribed Angles • An inscribed angle is an angle that has its vertex on the circle and its sides contained in chords of the circle.

  16. Inscribed angles Intercepted Arc

  17. Inscribed Angles Theorem • If an angle is an inscribed angle, then the measure is equal to ½ the measure of the intercepted arc or(the measure of the intercepted arc is twice the measure of the inscribed angle. • Inscribed angles

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