How to Center a Circle

Two Methods:The tutorialHelpful Guidance

This article shows a very quick way to approximate a circle's center. All that is needed is a circle to be centered, a writing implement tool and a 90 degree angle from a business card, paperback book corner, etc, if your "tool" has a good right angle. However, we'll use Excel's media box tool and select the shapes we need from it to construct the required diagram.

Method 1
The tutorial

  1. Image titled Center a Circle Step 2
    1


    Open a new Excel workbook and, using the Media Browser tool Shapes option, draw a circle, and draw any two different right angles you like, i.e.
    so long as their vertex and two endpoints do not coincide, but all three points do fall on (intersect) the circumference of the circle.
  2. 2
    Notice that their two hypotenuses, are different line segments, and will each bisect the circle. Thus, the hypotenuses being diameters meet (intersect) at exactly one point -- the center of the circle! Done!
    Circle with 2 Right Angles Finding the Center

Method 2
Helpful Guidance

  1. 1
    Make use of helper articles when proceeding through this tutorial:

Tips

  • This works because any "inscribed" 90 degree angle bisects the inscribing circle. More specifically, when we draw the 90-degree angle vertex touching the curve, thus forming a right triangle, then the arc of the circle that the hypotenuse intersects will measure 180-degrees. That makes the hypotenuse of any inscribed right triangle to be a diameter of the circle. When you draw two non-concurrent triangles, you'll have/get two different (distinct) diameters of that circle. And the diameters of the same circle can only intersect at the center of the circle.
  • This method is simple because a right-angle is a very common tool in many practical applications, and the drawing can be easily MacGyvered (rigged, ad hoc) out of your environment using a handy business card, Post-it Note, paperback book cover, etc. It's almost "foolproof".
  • Incidentally the ratio of the interior angle of an arc to the inscribed angle that intersects that arc is 2:1, and for example in an inscribed 29, 61, 90 rt triangle, the 29 degree base angle cuts off a 58 degree arc and the 61 degree base angle cuts off a 122 degree arc, (29*2) + (2*61) = 58 + 122 = 180. The sides of any 180 degree angle lie upon and define a straight line.

Sources and Citations

  • Michael Woods, Caltech alum, Physicist, Entrepreneur .. answering the question, "How Do You Find the Center of a Circular Disk?" on Quora.com, 11/08/14

Article Info

Categories: Mathematics | Geometry