Secant and Tangents

Cards (29)

  • Formula if given the arc and on the circle
    Arc/2
  • Formula if given the arc and in the circle
    Arc + Arc/2
  • Formula if given the arc and out of the circle
    B Arc - S Arc/2
  • Formula if given the angle and intersects inside
    ab = cd
  • Formula if given the angle and intersects outside with 3 given
    a^2 = b(b+c)
  • Formula if the angle is given and intersects outside
    a(a+b) = c(c+d)
  • c is on top

    intersects outside
  • Exercises
    Find the center and radius of the circle represented by each equation
  • Life Performance Outcome

    • I am a courageous, resourceful explorer and problem solver, demonstrating my creativity and charisma
  • Standard Form of the Equation of a Circle
    • π‘₯ βˆ’ β„Ž 2 + 𝑦 βˆ’ οΏ½οΏ½ 2 = π‘Ÿ2
    • Center: (β„Ž, π‘˜)
    • Radius = π‘Ÿ
  • Given the center and radius of circles, determine the center-radius form
  • Intended Learning Outcomes in Coordinate Geometry
    • I can illustrate the center-radius form of the equation of a circle
    • I can determine the center and radius of a circle given its equation and vice versa
    • I can solve problems involving geometric figures on the coordinate plane
  • Exercises
    • π‘₯ βˆ’ 3 2 + 𝑦 βˆ’ 5 2 = 4
    • π‘₯2 + οΏ½οΏ½2 = 9
    • π‘₯ + 4 2 + 𝑦 βˆ’ 7 2 = 81
    • π‘₯2 + 𝑦 + 2 2 = 5
    • π‘₯2 + 𝑦2 = 3
    • π‘₯ βˆ’ 7 2 + 𝑦 βˆ’ 9 2 = 25
    • π‘₯ + 2 2 + 𝑦2 = 16
    • π‘₯ βˆ’ 12 2 + 𝑦 + 6 2 = 2
    • Given the center and radius of the following circles, determine the center-radius form: 1. Center 3, βˆ’4 ; π‘Ÿ = 4
    • Center (5,1); π‘Ÿ = 3
  • Illustrating the center-radius form of the equation of a circle
    Ability to illustrate the center-radius form of the equation of a circle
  • Exercises
    • Given the center and radius of circles, determine the center-radius form:
    • Center: -8, -3; Radius: 3
    • Center: (6, -9); Radius: 1/4
    • Center: -7, 4/5; Radius: 6
    • Center: -2/3, -3/8; Radius: 2/3
    • Center: -5, -1; Radius: 3
    • Center: 10, -3; Radius: 2 3
    • Center: 3.6, -2.5; Radius: 2 6
    • Center: 4.5, 1.9; Radius: 3 5
  • Determining the center and radius of a circle

    Ability to determine the center and radius of a circle given its equation and vice versa
  • Answer: Part I (2, 6, 7) and Part II (2, 7, 9) of Worksheet 11 – Center-Radius Form of the Equation of a Circle (pages 83–84)
  • Solving problems involving geometric figures on the coordinate plane
    Ability to solve problems involving geometric figures on the coordinate plane
  • Exercise 3.9
    Given the center and radius of circles, determine the center-radius form
  • EXERCISES

    Determine the general equation of the given circle given its center and radius
  • Exercise 3.8
    Determine the center and radius of circles with equations in center-radius form
  • Illustrating the center-radius form of the equation of a circle
  • Determining the center and radius of a circle given its equation and vice versa
  • Center and radius
    • Center: (3, -3), Radius: 4 units
    • Center: (-2, -1), Radius: 7 units
    • Center: (2, 1), Radius: 4 units
    • Center: (-1, -4), Radius: 2 units
    • Center: (-2, -6), Radius: 5 units
  • Solving problems involving geometric figures on the coordinate plane
  • Equation of a circle given its center and radius

    Center is given as (h, k) and radius as r
  • Additional exercises provided for determining the general equation of circles given their center and radius
  • Rewriting general equations of circles to center-radius form
    • (x - 2)^2 + (y + 5)^2 = 4^2
    • (x - 4)^2 + (y + 1)^2 = 7^2
    • (x + 5)^2 + (y - 7)^2 = 4^2
    • (x + 1)^2 + (y + 2)^2 = 2^2
    • (x + 2)^2 + (y + 8)^2 = 5^2
  • Determining the center and length of the radius from the general equation of circles