Secant and Tangents

• 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

  • 𝑥 − ℎ 2 + 𝑦 − �� 2 = 𝑟2
  • Center: (ℎ, 𝑘)
  • Radius = 𝑟
• 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

  • 𝑥 − 3 2 + 𝑦 − 5 2 = 4
  • 𝑥2 + ��2 = 9
  • 𝑥 + 4 2 + 𝑦 − 7 2 = 81
  • 𝑥2 + 𝑦 + 2 2 = 5
  • 𝑥2 + 𝑦2 = 3
  • 𝑥 − 7 2 + 𝑦 − 9 2 = 25
  • 𝑥 + 2 2 + 𝑦2 = 16
  • 𝑥 − 12 2 + 𝑦 + 6 2 = 2
  • Given the center and radius of the following circles, determine the center-radius form: 1. Center 3, −4 ; 𝑟 = 4
  • Center (5,1); 𝑟 = 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