Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Regular polygons inscribed in a circle
Construct equilateral triangles squares and regular hexagons in circles
Problem types
- Reason about polygons inscribed in a circle
Builds on
- Constructions with compass and straightedge
- Angle sums and exterior angles · Useful idea
Angles of a polygon in a circle are found by splitting it into triangles whose angles sum to 180 degrees.
Leads to
- The incircle and the circumcircle · Extend the idea
The circle through the vertices of a regular inscribed polygon is its circumscribed circle, the circle whose center is where the perpendicular bisectors of the sides meet.
- The complex plane · See it applied
The vertices of a regular polygon in a circle are complex numbers of equal modulus separated by equal angles.
- Area from two sides and the included angle · See it applied
A regular polygon inscribed in a circle splits into congruent triangles whose area uses the sine of the central angle.
Related skills
- A tangent from a point outside a circle · Shared foundations
Open the interactive map to explore lessons and skill connections.