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Circles

Circles. Chapter 10 Sections 10.1 –10.2. Notes. On your notes handout you will see space to do practice problems. Next to each slide, solve the problem from the practice slide that follows it. F. Parts of a Circle. Circle F. F. center. Use the center to name a circle. Parts of a Circle.

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Circles

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  1. Circles Chapter 10 Sections 10.1 –10.2

  2. Notes • On your notes handout you will see space to do practice problems. • Next to each slide, solve the problem from the practice slide that follows it.

  3. F Parts of a Circle Circle F F center Use the center to name a circle.

  4. Parts of a Circle chord tangent secant diameter *a diameter is also a chord radius Segments & Lines

  5. Name the parts of the circle A AB ______ CF ______ ED ______ line m _____ line l ______ m l B C F E D

  6. Central angles Central angle - Vertex is on the center.

  7. MNO MO MON Types of Arcs major arc minor arc semicircle M P O N

  8. Measure of Arcs & Angles minor arc = its central angle major arc = 360 - its central angle 68° 360 – 68 = 292 68° 292°

  9. Find the measure of each arc A AC = 120 B ABC = C

  10. Measure of Arcs & Angles semicircle = 180 Diameters create semi-circles 180°

  11. Find each measure is a diameter. mNCL = R M mRCL = x - 1 60 3x + 5 mRCM = N C L mRCN =

  12. STOP HERE!!

  13. Formulas • Radius/diameter • Circumference radius = ½diameter r = ½ d diameter = 2(radius) C = 2∏r or C = ∏d

  14. Find the missing measures using the given measurements. 6. r = 7mm, d = ? , C = ? 7. C = 26 mi, d = ?, r = ? 8. d = 26.8 cm, r = ?, C = ?

  15. Arc Length l = arc length Arc length is part of the circumference of a circle l =A x C 360 Where A = measure of the central angle & C = circumference 68°

  16. Find the arc length l = arc length C AC = 9 cm and mCBD=40 Find the length of arc CD. B A D 40° Questions involving arc length should ALWAYS use the word length in the question.

  17. Very important!!!! Arc LENGTH (l) is not the same as the DEGREE measurement of the arc (m). If you are asked for the measurement of the arc, that is the degrees.

  18. Stop here. The rest of this powerpoint presentation focuses on Lesson 10-3 and 10-4.

  19. LESSON 12-2ARCS and CHORDS

  20. A C B D then AB CD Arc and Chord Relationships If chords are congruent, then arcs are congruent.

  21. A C B D mAB = mCD Congruent central angles have congruent arcs. móCPD=110ô móAPB=110ô P

  22. A C B D Congruent central angles have congruent chords. móCPD=110ô móAPB=110ô AB=CD P

  23. A O C P R B D Arc and Chord Relationships Two chords are  if and only if they are the same distance from the center.

  24. A G H B Arc and Chord Relationships If a diameter is perpendicular to a chord, then it bisects the chord. K

  25. A G H B Arc and Chord Relationships Radius KH is perpendicular to chord AB. AB is 16 cm long. K Find BC. C

  26. G Q E P R H F Arc and Chord Relationships Chords EF and GH are equidistant from the center. If the radius of circle P is 15, and EF = 24, find PR and RH.

  27. A G H B AH  BH Arc and Chord Relationships If a diameter is perpendicular to a chord, then it bisects the arc. K

  28. A G H B Arc and Chord Relationships Radius KH is perpendicular to chord AB. If mBH = 53 find mHA and m AG K C mHA= 53, mAG= 127

  29. Lesson 10-4 Inscribed Angles

  30. Inscribed angles • Vertex is on the circle.

  31. Measure of Arcs & Angles inscribed angle = ½minor arc 34° 68°

  32. Find the measure of each arc or angle ? = 56 ?° 28° 88° ?° ? =44

  33. Inscribed angles of the same arc or congruent arcs are congruent angles. A B Since both angles cut off arc DC, they are congruent. C D

  34. B A C F D E Arcs FE and DC are congruent, so the angles are also congruent.

  35. If an inscribed angle intercepts a semi-circle, the angle is a right angle.

  36. If a quadrilateral is inscribed in a circle, then the opposite angles are supplementary. If m = 42, find m W X Z Y

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