A (regular) hexagon is drawn so that its vertices are on the circumference of a circle. Radius:8.5cm?

Question

Calculate the distance from the centre of the circle to the centre of one edge of the hexagon. Please explain + working out :-) fanks

Answer 1

the anwser is 8.5cm itself.

Answer 2

I misread the first time

If you break the hexagon into 6 equal isosceles triangles

The distance from the center of the circle is equal to one edge of a right triangle that is created if you bisect the inner vertex of the triangle. So using trig functions.

The bisected angle gives us a 30 degree angle so

cos (30degrees)  = adjacent/hypotenuse

hypotenuse = 8.5 cm

0.866 = adj./8.5

adj = 7.36 cm, This is the length to the center of the edge.

I added a link to a diagram I did to help explain how I got my answer.

Answer 3

You are looking for the apothem of the hexagon.

The hexagon can be divided into six isosceles triangles. The apex of each triangle is 60°, so the triangles must be equilateral with sides of length 8.5 cm.

The apothem divides one of the equilateral triangles into congruent right triangles with hypotenuse 8.5 cm and base 4.25 cm.

By the Pythagorean theorem,

4.25² + apothem² = 8.5²

apothem² = 54.2

apothem = 7.361 cm

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