Complement the circular diagram, which shows that 5 m was cut off from a 30 m wire

Complement the circular diagram, which shows that 5 m was cut off from a 30 m wire, that is, the length of 30 m was reduced by 5 m.

Suppose a wire with a length of 30 m is circular. The circumference L and its radius R are interconnected by the ratio:

L = 2πR,

from here we can determine the radius of the circle if its length is known:

R = L / (2π);
R ≈ 30 / (2 * 3.14);
R ≈ 4.77 (m).

Divide a circle into six equal parts
Let’s say a piece of AB 5 m long was cut from a wire 30 m long, which is

5/30 = 1/6

part of a circle.

If we divide the whole circle into 6 equal parts, then we get a regular hexagon ABCDEF. Since the inscribed angle AOB rests on the arc ALB, which is 1/6 of the circle, then its degree measure is:

∠AOB = 360 °: 6 = 60 °.

But since the sides AO and BO of the triangle AOB are the radii of the circle, then in the triangle AOB the angles at the base are equal:

∠ABO = ∠BAO = (180 ° – ∠AOB) / 2 = (180 ° – 60 °) / 2 = 120 ° / 2 = 60 °.

Thus, the triangle AOB is equilateral, the side of which is equal to the radius of the circle:

AB = AO = BO = R = 4.77 (m).

It follows from this that the side of a regular hexagon inscribed in a circle ABCDEF is also equal to the radius of the circle. Therefore, in order to cut a piece 5 m long from a wire 30 m long, it is necessary to divide the circle into 6 equal parts, constructing a regular hexagon, the side of which is equal to the radius of the circle.

In conclusion, note that the length of the arc ALB and the side AB of the triangle ABO, as can be seen from the figure, differ insignificantly:

ALB – AB = 5 – 4.77 = 0.23 (m).