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CIRCLES 2

CIRCLES 2. Moody Mathematics. ANGLE PROPERTIES:. Let’s review the methods for finding the arcs and the different kinds of angles found in circles. Moody Mathematics. The measure of a minor arc is the same as…. …the measure of its central angle. Moody Mathematics. Example:.

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CIRCLES 2

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  1. CIRCLES 2 Moody Mathematics

  2. ANGLE PROPERTIES: Let’s review the methods for finding the arcs and the different kinds of angles found in circles. Moody Mathematics

  3. The measure of a minor arc is the same as… …the measure of its central angle. Moody Mathematics

  4. Example: Moody Mathematics

  5. The measure of an inscribed angle is… …half the measure of its intercepted angle. Moody Mathematics

  6. Example: Moody Mathematics

  7. The measure of an angle formed by a tangent and secant is … …half the measure of its intercepted arc. Moody Mathematics

  8. Example: Moody Mathematics

  9. The measure of one of the vertical angles formed by 2 intersecting chords ...is half the sum of the two intercepted arcs. Moody Mathematics

  10. Example: Moody Mathematics

  11. The measure of an angle formed by 2 secants intersecting outside of a circle is… …half the difference of the measures of its two intercepted arcs. Moody Mathematics

  12. Example: Moody Mathematics

  13. The measure of an angle formed by 2 tangents intersecting outside of a circle is… …half the difference of the measures of its two intercepted arcs. Moody Mathematics

  14. Example: Moody Mathematics

  15. PROPERTIES: Complete the theorem relating the objects pictured in each frame. Moody Mathematics

  16. Note: Many of our theorems begin the same way, “In the same circle, or in congruent circles…” Moody Mathematics

  17. So: We will just start “In the same circle*…” where the * represents the rest of the phrase. Moody Mathematics

  18. All radii in the same circle,* … ...are congruent. Moody Mathematics

  19. In the same circle,* Congruent central angles... ...intercept congruent arcs. Moody Mathematics

  20. In the same circle,* Congruent Chords... ...intercept congruent arcs. Moody Mathematics

  21. Tangent segments from an exterior point to a circle… ...are congruent. Moody Mathematics

  22. The radius drawn to a tangent at the point of tangency… ...is perpendicular to the tangent. Moody Mathematics

  23. If a diameter (or radius) is perpendicular to a chord, then… ...it bisects the chord… …and the arcs. Moody Mathematics

  24. In the same circle,* Congruent Chords... ...are equidistant from the center. Moody Mathematics

  25. Example: Given a circle of radius 5” and two 8” chords. Find their distance to the center. Moody Mathematics

  26. If two Inscribed angles intercept the same arc... ...then they are congruent. Moody Mathematics

  27. If an inscribed angle intercepts or is inscribed in a semicircle … ...then it is a right angle. Moody Mathematics

  28. If a quadrilateral is inscribed in a circle then each pair of opposite angles … ...must be supplementary. (total 180o) Moody Mathematics

  29. If 2 chords intersect in a circle, the lengths of segments formed have the following relationship: Moody Mathematics

  30. Example: Moody Mathematics

  31. If 2 secants intersect outside of a circle, their lengths are related by… Moody Mathematics

  32. Example: Moody Mathematics

  33. If a secant and tangent intersect outside of a circle, their lengths are related by… Moody Mathematics

  34. Example: Moody Mathematics

  35. Let’s Practice!

  36. Example: Given Moody Mathematics

  37. Example: Moody Mathematics

  38. Example: Moody Mathematics

  39. Example: Moody Mathematics

  40. Example: Given a circle of radius 13” and two 24” chords. Find their distance to the center. Moody Mathematics

  41. Example: Moody Mathematics

  42. Example: Moody Mathematics

  43. Example: Moody Mathematics

  44. Example: Moody Mathematics

  45. Example: Moody Mathematics

  46. Example: Moody Mathematics

  47. Example: Of the following quadrilaterals, which can not always be inscribed in a circle? • Rectangle • Rhombus • Square • Isosceles Trapezoid

  48. Example: Moody Mathematics

  49. Example: Moody Mathematics

  50. Example: Regular Hexagon ABCDEF is inscribed in a circle. Moody Mathematics

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