The need to determine the center of the circle occurs not only during the solution of planimetic problems on geometry. Practical construction and calculations also often enter the deadlock when it is impossible to determine the center of the circle. What actions (using measuring instruments and without) should be made to calculate the location of the desired center?
Definition of the center of the circle using the ruler
The center inscribed in the quadrilateral of the circle lies at the point of intersection of its bisector. It is known that the diagonal of the parallelogram is bisectors of its corners. Therefore, the approval is true:
"The center of the circle that is inscribed in the parallelogram will be located at the point of intersection of the latter diagonals." The rectangle, rhombus and square are partial cases of the parallelogram, so this approval will also be fair for them.
So, there is a circle, the center of which must be determined.
Stages of construction:
- Take an arbitrary point on the circle. Spend a tangent to the circumference through it.
- Next, spend the second tangent so that it forms it to form with the first sharp or straight angle. There will be no error if this angle is blunt. However, for the purposes of further construction, such a "picture" will be more difficult.
- Through other circumference points, spend 2 more tangents parallel to the first two.
- As a result, get a parallelogram (because the parties lie on parallel direct by construction), describing the circle.
- Connect the opposite vertices of the obtained quadrangular figure. Received 2 diagonals.
- Point intersection of these segments and will be the center of a given circumference.
Defining the center of the circle using the stencil
This method is especially in demand if it is necessary to find a center with a separate round part.
The justice of the actions described below is based on approval that the center of the circle described near any triangle will be located at the point of intersection of its median perpendicular. In the particular case, when it comes to a rectangular triangle, the center of the circumference described near it will be in the middle of the hypotenuse.
So, in front of you a circle, the center of which is necessary to determine.
Stages of construction:
- Take an arbitrary sheet of paper. It is he who will act as the main pattern in the course of determining the center of the circle.
- For further constructions, the prerequisite is the presence of your direct corner template. If you have not taken album or a notebook (which the sides of which are located by default under ∠90 °), a straight angle must be formed by making the necessary bends.
- Next, install the vertex of a direct angle on the circumference arc.
- At points where the sides of this direct corner crossed the circle, set the mark. Swipe through them straight.
- The resulting segment is a hypothenucleosis of a rectangular triangle. Consequently, it lies the center of your circumference. If there is a ruler at hand, measure the meaning of this hypotenuse, finding the desired point.
- If no measuring device is near, continue to build. Install the vertex of the direct angle (template) to another circumference point. Re-mark the points of intersection of the side of the angle and the circumference.
- By connecting them by a segment, you get another hypothen of the rectangular triangle. A given circle is also described around this triangle.
The desired center of the circle lies on the hypotenuse of both the first and second triangle. These segments have 1 total point - the point of their intersection. So the center of the specified circle lies at this point.
Definition of the center of the circle
To find the center of a circle cut out of paper, it suffices to perform such actions:
- Bend a round blank in half.
- Next, the semicircle received bent once again in half.
- As a result, get 4 bends, the intersection point of which will be the center of your circle. If desired, the number of folds can be increased, but for the purposes of the task, there will be enough 4.
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