Lesson: Positions of Points, Straight Lines, and Circles with respect to Circles Mathematics

Students will be able to

• recognize how a point relates to a circle (i.e., whether a point lies inside, outside, or on the circle) and how line segments drawn between the circle’s center and this point relate to the radius of the circle,
• recognize how a line relates to a circle (i.e., whether it is a secant, a tangent, or outside the circle),
• use the relationships between points and circles and between lines and circles to form and solve linear equations and inequalities,
• understand that a tangent is perpendicular to a radius at the point of tangency and understand the converse to this: if a line is perpendicular to the diameter of a circle at one of its endpoints, then it must be a tangent to the circle,
• recognize how two circles relate to each other,
• find unknown lengths and angles relating to geometric constructions of circles and straight lines where
  • a circle and at least one radius are given,
  • a circle and at least one diameter are given,
  • a circle and at least one tangent are given,
  • a circle and at least one chord are given,
  • at least two circles are given and share a common center,
  • at least two circles are given and intersect,
  • at least two circles are given and touch (either on the inside or on the outside).