Inscribed Polygons

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

Inscribed Polygon

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

Inscribed Equilateral Triangle

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

formulas

formulas

Formula for the Side of an Inscribed Equilateral Triangle

Example

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

Inscribed Equilateral Triangle

formulas

formulas

formulas

Side of an Inscribed Square

Inscribed Square


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

Formula for the Side of an Inscribed Square

Example

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

Inscribed Square


operaciones

Apothem of an Inscribed Hexagon

Inscribed Hexagon


formulas

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.

Inscribed Hexagon