Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4785. (March 2016)

B. 4785. $\displaystyle \mathcal{G}$ is a given sphere in the space. For any line $\displaystyle e$ that has no common point with $\displaystyle \mathcal{G}$, define the line $\displaystyle f$ as the conjugate of $\displaystyle e$ with respect to $\displaystyle \mathcal{G}$ if $\displaystyle f$ joins the points of tangency on the two planes tangent to $\displaystyle G$ passing through $\displaystyle e$. Show that two lines of the space passing $\displaystyle \mathcal{G}$ are skew if and only if their conjugates with respect to $\displaystyle \mathcal{G}$ are skew.

(5 pont)

Deadline expired on April 11, 2016.

### Statistics:

 26 students sent a solution. 5 points: Baran Zsuzsanna, Döbröntei Dávid Bence, Fuisz Gábor, Gáspár Attila, Glasznova Maja, Kerekes Anna, Lajkó Kálmán, Matolcsi Dávid, Polgár Márton, Sudár Ákos, Tiszay Ádám, Zólomy Kristóf. 4 points: Bukva Balázs, Csahók Tímea, Cseh Kristóf, Hansel Soma, Tóth Viktor. 3 points: 2 students. 2 points: 1 student. 1 point: 2 students. 0 point: 4 students.

Problems in Mathematics of KöMaL, March 2016