Consider a regular hexagon inscribed in circle c with radius r. regular hexagons have six congruent sides and six congruent angles. 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 .

∠ACB=60°, AC=r, Perimeter=6r units, Circumference=6.28r≈6r

Step-by-step explanation:

Given a regular hexagon inscribed in circle C with radius r. Also, ∠CAB = 60°.  

In ΔACB,

∠CAB = 60° and also ∠CAB=∠CBA as CA=CB (both radii of same circle) ∴ ∠CBA=60°

By angle sum property of triangle

∠CAB+∠CBA+∠ACB=180°

⇒ 60°+60°+∠ACB=180°

⇒ ∠ACB=60°

All angles of ΔABC are equal which implies ABC is an equilateral triangle.

∴ AB=BC=AC=r

Perimeter of hexagon=6(Length of one side of hexagon)

                                     =6(AB)=6r units

Circumference of circle==2(3.14)r=6.28r≈6r units

∴Perimeter of hexagon is equal to circumference of circle.

Circumference of circle is =2(3.14)r=6.28r units

Hence, ∠ACB=60°, AC=r, Perimeter=6r units, Circumference=6.28r≈6r

1) 60

2) r

3) 6r

4) slightly less than

5) slightly greater than 6r