Prove or Disprove Points on a Circle
...
Subject Area: Mathematics (B.E.S.T.) | Grade Level: 10
Lesson Length: 45 minutes
Keywords/Tags: Points on a circle
Lesson Description: In this lesson, students will investigate methods for proving or disproving whether a given point lies on a circle. The lesson will explore both analytical and geometrical approaches for verifying whether a point lies on a circle. Analytical methods will involve the use of algebraic equations and formulas to determine whether a point satisfies the equation of the circle. These methods will include using the distance formula to calculate the distance between the point and the center of the circle, as well as using the equation of the circle to solve for the coordinates of the point. Geometrical methods will involve constructing and analyzing various geometrical figures. These methods will include using the Pythagorean theorem to calculate lengths, as well as using angle relationships and properties of parallel and perpendicular lines.

  • Other MGSE9-12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.rnFor example, prove or disprove that a figure defined by four given points in therncoordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circlerncentered at the origin and containing the point (0,2).
Views: 271 Favorited: 0 Reviews: 0 Review Status: Published (Public)
Video : How to Prove that a Point Lies on a Circle (or Inside/Outside)
Instructions: Please watch the following video as many times as needed before starting to go through other lesson pages. Understanding the content of the video is very important since the lesson activities will be all about this video content.Please watch the following video as many times as needed before starting to go through other lesson pages. Understanding the content of the video is very important since the lesson activities will be all about this video content.")
Description: Learn how to prove or disprove that a point lies on a circle.
Quiz : Prove or Disprove Points on a Circle
Instructions: Please complete this quiz by choosing the correct answer for each question. You can take this quiz as many times needed.
Question #1

What is the equation of the circle with center (2, 3) and radius 5?

Question #2
A point (4, -1) lies on the circle with center (-2, 5) and radius 7. True or False?
Question #3

Which of the following statements is equivalent to proving that a point lies on a circle?

Question #4

What is the radius of the circle with equation (x - 4)^2 + (y - 1)^2 = 16?

Question #5
How do you use the Distance Formula to determine whether a point lies on a circle?
Question #6
Given the point (4, -1), is it on the circle with center at (0, 0) and radius 2?
Question #7
What is the distance between the center of the circle with equation (x - 1)^2 + (y + 2)^2 = 25 and the point (-3, -4)?
Question #8
If the circle has equation (x - 3)^2 + (y + 2)^2 = 16, does the point (6, -2) lie on the circle? Explain.
Question #9
If a point lies on a circle, what is the relationship between the coordinates of the point and the equation of the circle?
Question #10
If a point lies inside a circle, what can you say about its distance from the center of the circle?
Resources : Points Inside/Outside/On a Circle
Instructions: Please see additional external resources below. Feel free visit each link to learn more about this lesson.
Khan Academy Points Inside/Outside/On a Circle Video
Use the distance formula to determine if a point lie inside, outside, or on a circle.
Khan Academy Points Inside/Outside/On a Circle Practice
Practice using the distance formula to determine if a point lies on the inside, outside, or on a circle.
CK-12 Geometry Flexbook Circles in the Coordinate Plane
Use the CK-12 Geometry Flexbook to learn more about circles in the coordinate plane. After reading through the lesson, use the green "Start Practice" button to to practice.