Three tangent theorem in view of the protective and affine geometry. Three tangent theorem is the essential theorem for de Casteljau algorithm used in computational geometry. The proof of this theorem is omitted in most of the literature. Presented paper contains three different proofs of this theorem. The first uses the method of projective geometry to prove four tangent theorem and then the three tangent theorem as its corollary. The second proof uses central projection of conic sections. The third proof is an affine analytic proof.