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:

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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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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