Analytic geometry

Spheres and circles in space

Sphere equation, relative positions, tangent planes and circles — up to Abitur+

Final two years of upper secondary school and exam preparation. Spheres are not part of every syllabus.

The booklet starts with the sphere equation, then point and sphere, sphere and line, sphere and plane. It continues with tangent planes and circles in space. The chapters Application, Abitur, Transfer and Abitur+ raise the level step by step. Every problem comes with two hints, an approach, the full solution and the typical mistake.