The Hexagon Inside

Part of the Circles section of Coddy's Geometry journey. Lesson 4 of 59.

How many diameters does it take to go once around a circle? Put a regular hexagon inside the circle, with its six corners on the circle. A regular hexagon has six equal sides and six equal angles. Measure the hexagon first.

Draw a radius to each of the six corners. The six angles at O share the full turn of 360°: $\frac{360}{6} = 60^{\circ}$ each.

Two sides of each triangle are radii, so they are equal. A triangle with two equal sides is isosceles.

$Circle O with six radii, six equal angles of 60 degrees at the center$

Challenge

ABCDEF is a regular hexagon with its corners on circle O. The radius OA is 5. Find the side AB. Then think: how many diameters long are six sides like it?

Then press Check.

Try it yourself

$Find the marked part of the figure$