Circumscribed and inscribed circles of triangles and regular polygons

MathematicsPlane GeometryAges 14–15

Drag the three vertices of a triangle: the circumcenter O is the intersection of the three perpendicular bisectors, the incenter I is the intersection of the three angle bisectors; the radii R and r and special cases (right triangle: O is the midpoint of the hypotenuse; equilateral triangle: O coincides with I) update instantly. Regular-polygon mode: change the number of sides n and drag a vertex to change the radius, revealing how R, r and side length a relate to each other.