Problem A. 446. (February 2008)
A. 446. The lengths of tangents drawn from the points A, B and C to a sphere s are a, b and c, respectively. T is a point on the sphere, not co-planar with A, B and C, such that .
Prove that the sphere passing through the points A, B, C, T touches s.
Deadline expired on March 17, 2008.
12 students sent a solution. 5 points: Korándi Dániel, Lovász László Miklós, Nagy 235 János, Nagy 314 Dániel, Nagy 648 Donát, Somogyi Ákos, Szabó 895 Dávid, Tomon István, Tossenberger Anna, Wolosz János. 4 points: Huszár Kristóf. 3 points: 1 student.