Finding the Center of a Circle

  • Context: MHB 
  • Thread starter Thread starter OSUstudent
  • Start date Start date
  • Tags Tags
    Center Circle
Click For Summary
SUMMARY

To find the center of a circle when the diameter is known and only a portion of the circle is visible, at least two distinct points on the circumference are required. By drawing a straight line between these two points and then constructing the perpendicular bisector of that line, the center can be determined. A second pair of points can be used to create another bisector, which will intersect at the center of the circle. This method provides a straightforward geometric approach to locating the center based on the known diameter and points on the circumference.

PREREQUISITES
  • Understanding of basic geometry concepts
  • Familiarity with the properties of circles
  • Knowledge of perpendicular bisectors
  • Ability to visualize geometric constructions
NEXT STEPS
  • Research geometric constructions using compass and straightedge
  • Learn about the properties of circle geometry
  • Explore coordinate geometry methods for circle center determination
  • Study the application of the midpoint formula in geometry
USEFUL FOR

Mathematicians, geometry students, educators, and anyone involved in geometric problem-solving will benefit from this discussion.

OSUstudent
Messages
10
Reaction score
0
Hello!

I have an application where I need to find the center of a circle where I am having trouble coming up with a simple way to do this. The diameter of the circle is known and i want to be able to determine the location of it where only a portion of the circle is known. (see the image below) I will know the location of a single point anywhere in the red circumference could anyone help me with this?
1623225283571.png
 
Mathematics news on Phys.org
Draw the straight line between two points on the circle. Draw the line bisecting that straight line. Do the same with a second pair of points. The two bisectors intersect at the center of the circle.
 
Thank you for your reply! I am looking for a formula that i could use to calculate where the center of the circle is based on the known diameter and a single point that resides in the red area. Sorry i should have meant to say in the original post that i was looking for a simple formula.
 
Runner74 said:
Thank you for your reply! I am looking for a formula that i could use to calculate where the center of the circle is based on the known diameter and a single point that resides in the red area. Sorry i should have meant to say in the original post that i was looking for a simple formula.

You're going to need at least two distinct points on the red arc of the circle to find its center.
 

Similar threads

MHB What is the Center and Radius of a Circle?
  • · Replies 9 ·
Replies
9
Views
2K
MHB Find the area of the shaded region
  • · Replies 2 ·
Replies
2
Views
1K
MHB Finding the Equation of a Tangent Circle with Center (3,5)
  • · Replies 2 ·
Replies
2
Views
2K
MHB How Do You Find the Equation of a Line Through a Point and a Circle's Center?
  • · Replies 6 ·
Replies
6
Views
2K
MHB The height of a section of overlapping circles.
  • · Replies 3 ·
Replies
3
Views
2K
MHB Equation of Circle in Standard Form
  • · Replies 6 ·
Replies
6
Views
2K
MHB How Do You Find the Equation of a Line Through a Point and a Circle's Center?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Finding the Equation of a Line through a Point and Circle Center?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Find the exact shaded area of the region in 4 overlapping circles
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Fitting circles inside other circles
  • · Replies 20 ·
Replies
20
Views
6K