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A polygon is inscribed in a circle if all its vertices are points on the circle and all sides are included within the circle.

All regular polygons can be inscribed in a circle.

The center of an inscribed polygon is also the center of the circumscribed circle.

The radius of the inscribed polygon is also the radius of the circumscribed circle.

### Side of an Inscribed Equilateral Triangle

By applying the Pythagorean theorem for one of the triangles, we obtain:

## Example

Calculate the length of the side of an equilateral triangle inscribed in a circle of 10 cm radius.

### Side of an Inscribed Square

By applying the Pythagorean theorem for one of the triangles, we obtain:

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## Example

Find the side of a square inscribed in a circle of 5 cm radius.

### Apothem of an Inscribed Hexagon

By applying the Pythagorean theorem for one of the triangles, we obtain:

Calculate the apothem of a hexagon inscribed in a circle of 4 cm radius.

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