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This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
This article has been viewed 60,269 times.
Finding the center of a circle can help you solve basic geometry problems like calculating perimeter or area. There are many methods to find the center of a circle. You can draw intersecting lines, intersecting circles, or you can use a ruler and a ruler.
Steps
Draw intersecting lines
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Draw a circle. Use the compass to draw a circle or trace a circular object. The size of the circle doesn’t matter. If you’re looking for the center of an existing circle, you don’t need to draw a new circle.
- A compass is an instrument designed to draw and measure circles. Buy a compass at your school or a stationery store! [1] X Research Source
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Draw a chord through two points on the circle. A chord is a line segment connecting two points on a circle. [2] X Research Source We call this chord AB.
- Consider using a pencil to draw straight lines. That way, you can erase the pencil strokes once you’ve found the center of the circle. Draw lightly to make it easier to erase.
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Draw the second chord. This line needs to be parallel and equal in length to the chord drawn earlier. Call the newly drawn line the chord CD. [3] X Research Sources
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Draw another line connecting the two points A and C. This third chord (the AC chord) will pass through the center of the circle; but we need to draw one more line to find the exact center of the circle.
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Connect B and D. Draw the last chord (BD) connecting the two points B and D. This line will cut the third chord (AC) just drawn.
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Find the center of the circle. If you draw the lines correctly, the center of the circle will be the intersection of the two lines AC and BD. [4] X Research Source Use a pen to mark the center of the circle. If you only need to find the center of the circle, delete the 4 chords you drew.
Use intersecting circles
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Draw a chord connecting 2 points on the circle. Use a ruler to draw a line inside the circle, side to side. The location of the selected points is not important. Call these two points A and B.
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Use a compass to draw two intersecting circles. These two circles must be the same size. Use point A as the center of one circle, and point B as the center of the other circle. Align these two circles to each other like a Venn diagram.
- Draw these two circles with a pencil, not with a pen. The job will be simpler if you can then delete these circles.
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Draw a vertical line through the two intersections of the circles. There will be a point on the top and a point on the bottom of the “Venn diagram” in the middle of the overlap of the circles. Use a ruler to make sure the line passes exactly through these points. Let C and D be the intersection points of the line just drawn and the first circle. This line segment is the diameter of the first circle.
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Delete two nested circles. This step will help make room for the next step. We now have a circle with two perpendicular segments passing through it. Don’t delete the two centers (A and B) of these circles! You will draw two new circles.
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Draw two new circles. Use a compass to draw two circles with equal radii: one with point C as center, and one with point D as center. As above, these two circles must also be nested like a Venn diagram. Remember: C and D are the intersections of the vertical line and the principal circle.
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Draw a line passing through the two intersections of the newly drawn circles. This horizontal line will cut through the overlap of the two new circles. This is also the second diameter of the first circle and will be perpendicular to the first diameter.
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Find the center of the circle. The intersection of the two diameters will be the exact center of the circle! Mark this point for comparison. If you want to make the drawing clean, you can erase all the diameters and extra circles.
Use a ruler and a ruler
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Draw two intersecting tangents of the circle. These two tangent lines are completely random. However, the job will be easier if you draw relatively perpendicular. [5] X Research Sources
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Translating the two tangent lines just drawn to form two lines parallel and opposite to the other side on the circle. You will have four tangent lines that form a parallelogram or almost a rectangle.
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Draw two diagonals of the parallelogram. The intersection of these two diagonals will be the center of the circle.
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Use a compass to check the accuracy of the center of the circle. The center of the circle will be correct if you do not deviate when translating straight lines or when drawing diagonal lines. You can delete parallelograms and diagonals.
Advice
- Try using square paper instead of white or horizontal paper. The squares will help when drawing perpendicular lines.
- You can also find the center of a circle using the “squared complement” math method. [6] X Research Source This is a useful method if you are given the equation of a circle, but does not work with the actual circle.
Warning
- A straight ruler is different from a tapered ruler. A straightedge can be anything straight and smooth, and a ruler with marks represents a unit of length. You can turn a ruler into a ruler by marking it in inches or centimeters.
- To find the exact center of the circle, you must use a compass and a ruler.
Things you need
- Pencil
- Paper
- Straight Ruler
- Compass
- Checkered paper
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This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
This article has been viewed 60,269 times.
Finding the center of a circle can help you solve basic geometry problems like calculating perimeter or area. There are many methods to find the center of a circle. You can draw intersecting lines, intersecting circles, or you can use a ruler and a ruler.
Thank you for reading this post How to Find the Center of a Circle at Lassho.edu.vn You can comment, see more related articles below and hope to help you with interesting information.
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