Consider a regular hexagon inscribed in circle C with radius r. Regular hexagons have six congruent sides and six congruent angl

Question

2 years ago

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Consider a regular hexagon inscribed in circle C with radius r. Regular hexagons have six congruent sides and six congruent angl

es. In the figure, angle CAB measures 60°.
What is m∠ACB?

°

What is the length of segment AB?

What is the perimeter of the hexagon?
The perimeter of the hexagon is

the circumference of the circle.

The circumference of the circle is

.

Mathematics

1 answer:

Leokris [45] · Answer 1 · 2023-05-05T14:03:59+03:00

The solution to the questions are:

The value of $< ACB\ is\ 60\textdegree$ . As a consequence, the radius of the circle is equal to the length of the segment AB.

AB = BC =CA = R. As a consequence, the radius of the circle is equal to the length of the segment AB.

The perimeter of the hexagon is equal to r times 6. As a result, the number 6r represents the hexagon's perimeter.

P=6.28r. As a result, the diameter of the circle is a fraction of a unit bigger than.

P=6.28r. As a result, the diameter of the circle is a fraction of a unit bigger than.

<h3>What is the length of segment AB?</h3>

1) Generally, the equation for m∠ACB is mathematically given as

CA= CB

CA = radius of the circle

Therefore,

∠CAB =

$\angle CBA = 60 \textdegree$

the sum of all the angles of a triangle

the sum of all the angles of a triangle is 180°

$< CAB + < CBA + < ACB = 180 \textdegree$

$60\textdegree + 60\textdegree + < ACB = 180\textdegree$

$120\tetxtdegree + < ACB = 180\tetxtdegree$

$< ACB = 60\textdegree$

The value of $< ACB\ is\ 60\textdegree$ .

2. What is the length of segment AB?

In the same manner, as in ACB, all of the angles are the same. As a result, we may say that the triangle has equal sides.

In a triangle with equilateral sides, each of the triangle's three sides has the same length.

AB = BC =CA = R

As a consequence, the radius of the circle is equal to the length of the segment AB.

<h3>3. What is the perimeter of the hexagon?</h3>

The formula for calculating the hexagon's perimeter is 6a, where an is the number of sides in the hexagon.

The circumference of the hexagon is equal to 6 times a.

The circumference of the hexagon is equal to six times each side (AB)

The perimeter of the hexagon is equal to r times 6.

As a result, the number 6r represents the hexagon's perimeter.

4. The perimeter of the hexagon is 6r the circumference of the circle.

the perimeter of the hexagon = 6r
the perimeter of the circle = $2 \pi$

$P=2*\pi*r$

P=2*3.14*r

P=6.28r

As a consequence of this, the hexagon's perimeter is less than the diameter of the circle.

5. The circumference of the circle is 6.28r.

the perimeter of the circle = $2 \pi r$

$P=2*\pi*r$

P=2*3.14*r

P=6.28r

As a result, the diameter of the circle is a fraction of a unit bigger than.