Mathematical and Physical Journal
for High Schools
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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 \frac{AT}{a}=\frac{BT}{b}=\frac{CT}{c}.

Prove that the sphere passing through the points A, B, C, T touches s.

(5 pont)

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.

Problems in Mathematics of KöMaL, February 2008