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How do you find the center of a circle if you're only given the equation?

David Jia
Math Tutor
David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

David Jia

Math Tutor

Expert Answer

The equation of a circle is (x-h)²+(y-k)²=r². The coordinates for the center of the circle are (h, k), so to find the center of the circle, solve for h and k.

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How do you find the center of the circle if you're only given the endpoints of the diameter?

David Jia
Math Tutor
David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

David Jia

Math Tutor

Expert Answer

If you're given two points that are the endpoints of the diameter of the circle, the midpoint of that line will be the center of the circle.

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Question

In the first method, what do I do if the chords are of different lengths?

Community Answer

It's not easy to construct parallel chords of equal length. In practice, it would be a process of trial and error until you get the chords you need. But the real goal here is to find the center of a circle, and here's a way to do it without worrying about equal and parallel chords: (1) draw any two or more chords; (2) perpendicularly bisect each chord (using either a compass or a ruler and right triangle; (3) the perpendicular bisectors will intersect at the circle's center.

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Question

What is the center of a circle?

Donagan

Top Answerer

It is the one point that is equidistant from all points on the circumference.

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If I use a compass to draw a circle, is the pivot point the center?

Donagan

Top Answerer

Yes, the point of a compass is placed at the center of a circle drawn by the compass. The object of this article, however, is to find the center of a circle that you have not drawn.

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How do I find the center of a circle using a pencil only, nothing else?

Donagan

Top Answerer

It cannot be done accurately. Imagine trying to do it with a very large circle.

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Question

Why not find the longest distance in the circle with a straight edge, divide the measurement in half, put a dot at that measurement you're done? No marks on the page, so simple.

Donagan

Top Answerer

While your method is quick and easy, it's not guaranteed to be absolutely accurate. There's a bit of guesswork involved. The methods described above introduce an element of guesswork, too, but they're designed to come extremely close to the center of the circle.

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Question

How do I find the center of a circular piece of wood? If I use your first method, how do I determine if lines AB and CD are parallel?

Community Answer

Measure the distance between the chords at opposite sides of the circle. If the distances are equal, the chords are parallel. Also, you can measure the lengths of the two diagonal lines (AD and BC). If those lengths are equal, the chords are parallel. In either case the chords do not have to be of the same length.

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I want to make a coin ring and need to find the center of a quarter dollar. It is tough to draw a lot of lines on the uneven surface. Any ideas?

Donagan

Top Answerer

Trace the outline of the coin on a piece of (heavy) paper. Locate the center of the paper circle. Punch a small hole through the center. Cut out the circle. Place it directly over the coin. Use a fine-tipped marking pen to mark the center through the paper.

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Is the point of intersection of two diameters of the same circle its centre?

Community Answer

Yes, the point of intersection is its center.

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Can't you draw two non parallel cords, find the center of each cord, draw perpendicular lines, they should intersect at the center?

Donagan

Top Answerer

Yes, that is true. The perpendicular bisector of any chord of a circle passes through the center of the circle.

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What is the run in inches for a rise of 5 inches at a 3% grade?

Donagan

Top Answerer

3% = 3/100 = 5" / x, where x is the run (in inches). By cross-multiplying, 3x = 500", and x = 166.67 inches.

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