A circle is a round figure that is made of all the points in a plane located away from a specific point, which is the center. However, in some cases, the center might not be marked.
When you find the center of the circle, you can make calculations like finding the circumference and area. You can also draw overlapping circles that you can paint or embroidery. Luckily, you can find the center of a circle using different methods.
The center of the circle will help you calculate the radius and diameter. This piece of information is necessary for several geometrical theories. It will also help you if you want to draw something on a circular wooden board or want to set up a central decorative piece in the center of a table.
Finding the Center of a Circular Object
You can find the center of a circular stool or table easily. This will help you if you want to draw something special or need to make a tablecloth. All you need is a framing square and a pencil or a marker.
Place the square on the top of the circle, making sure that the right angle touches the edge of the circle.
Mark the points where the sides of the square touch the edge of the circle.
Use the straight edge of the framing square to connect the 2 points together.
Repeat the process by repositioning the right angle so it touches the edge of the circle in another spot.
The 2 lines will cross at the center of the circle.
Finding the Center of a Drawn Circle
Things can be easier if you want to find the center of a circle that is drawn on paper.
Using Crossed Lines
For this method, you need a ruler and a pencil. You’ll also need a compass if you’re going to draw a circle.
Start by drawing a circle or use the circle you already have.
Draw a straight line to connect 2 opposite points along the edge of the circle using a pencil and a ruler. Name the points A and B and the line AB.
Draw another line or chord parallel to AB line, using the points C and D. Call the new line CD.
Join the 2 points A and C and draw a line called AC. This line will pass through the center of the circle. Do the same with points B and D. The new line BD will cross over AC.
The intersection point of AC and BD is the center of your circle. You can then erase the lines you drew to keep the center marked.
Using Overlapping Circles
You can actually find the center of a circle by drawing more circles. For this method, you’ll use a compass, in addition to a ruler and a pencil.
Mark 2 opposite points and label them A and B.
Draw a line between the 2 points.
Draw equal circles, making sure that they’re exactly the same size using your compass. Use point A as the center of the first circle and point B as the center of the second one. The 2 circles should overlap.
The 2 new circles will intersect in 2 points, one at the bottom and one at the bottom of the space between them.
Draw a line that passes through these 2 points and label them C and D. This line will be the diameter of the original circle.
Erase the 2 new circles you drew while maintaining the diameter you drew. As a result, you will have 2 perpendicular lines; AB and CD.
Draw 2 new circles. Use point C as the center of the first one and point D as the center of the new one. The new circles will overlap just like the old ones.
Repeat the same process with the 2 new circles. Draw a line through the 2 points at which the new circles intersect. It will be the second diameter of the original circle and should be exactly perpendicular to the first diameter.
The center of the original circle will be the point where the 2 diameters intersect. Erase all the extra circles and diameters, and you will have the center of the original circle marked.
Using a Triangular Ruler and Straightedge
For this method, you won’t have to draw any circles, but you’ll use a straightedge and a ruler to draw straight lines.
Start by drawing a line that touches the outer edge of the circle.
Draw another line that is perpendicular to the first line. It should also touch the outer edge of the circle. The 2 lines should intersect and create what looks like a corner of a square or rectangle.
Draw 2 more lines on the opposite sides of the circle. Finally, you will end up with what looks like a rectangle or square.
Draw the diagonals of this new shape. The 2 diagonals will intersect at the center of the original. You can check the accuracy of the circle using the compass.
Erase all the extra lines to be left with the original circle.