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Exploring Circle Properties: Central vs. Inscribed Angles

This unit delves into the special properties of circles, including central and inscribed angles, chords, diameters, and radii. Understand the distinctions between these elements and how they relate to each other. Test your knowledge on circle concepts!

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Exploring Circle Properties: Central vs. Inscribed Angles

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  1. Monday December16

  2. Test Friday

  3. Analytic Geometry UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question: How are central angles different from inscribed angles? Standard: MM2G3.b

  4. C Parts of a Circle Circle – set of all points _________ from a given point called the _____ of the circle. equidistant C center Symbol:

  5. CHORD: A segment whose endpoints are on the circle

  6. DIAMETER: Diameter Distance across the circle through its center P Also known as the longest chord.

  7. Radius RADIUS: Distance from the center to point on circle P

  8. D = 24 32 12 r = ? 16 r = 4.5 6 D = 12 9

  9. Q R P S T Use P to determine whether each statement is true or false.

  10. Secant Line: intersects the circle at exactly TWO points SECANT sounds like second

  11. Tangent Line: a LINE that intersects the circle exactly ONE time Forms a 90°angle

  12. Name the term that best describes the notation. Secant Radius Diameter Chord Tangent

  13. Arc Length • A portion of the circumference of the circle – as if you used a ruler to measure the length A B

  14. THINGS TO REMEMBER: A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal Linear Pairs are Supplementary

  15. Central Angle : vertex is at the center of the circle A P C B APB is a Central Angle

  16. Case I:Vertex is AT the center A P C B

  17. EDF Semicircle: An Arc that equals 180° To name: use 3 letters E D P F

  18. Central Angle : vertex is at the center of the circle ACB AB A Major Arc Minor Arc More than 180° Less than 180° P C B

  19. measure of an arc = measure of central angle m AB m ACB m AE A E 96 Q = 96° B C = 264° = 2x + 14 Find x. x = 35

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