A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.

The diameter is a straight line drawn through the center and having its extremities in the curved surface. The radius - 1/2 diameter - is the straight line from the center to a point on the surface.

A plane is tangent to a sphere when it touches the sphere in only one point. A plane perpendicular to a radius at its outer extremity is tangent to the sphere, Fig. 83.

Fig. 83. Plane Tangent to Sphere.

Fig. 84. Great and Small Circle.

An inscribed polyhedron is a polyhedron whose vertices lie in the surface of the sphere.

A circumscribed polyhedron is a polyhedron whose faces are tangent to a sphere.

A great circle is the intersection of the spherical surface and a plane passing through the center of the sphere, Fig. 84.

Fig. 85. Intersections of Plane with Cone and Cylinder Giving Ellipses as Shown in (b) and (d).

A small circle is the intersection of the spherical surface and a plane which does not pass through the center, Fig. 84.