Circles inscribed in and circumscribed about regular polygons
Answers are for parents and teachers.
1
What is the circumradius of a regular hexagon with side 18?
18
2
What is the side of a square inscribed in a circle of radius 4?
4√2
3
What is the incircle radius of a regular triangle with side 2√3?
1
4
A regular hexagon has side 4 and apothem 2√3. What is its area?
24√3
5
Why is the diagonal of a square inscribed in a circle equal to the diameter?
The 90° inscribed angle subtends a diameter, so the diagonal passes through the centre.