Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4704. (March 2015)

B. 4704. The circles $\displaystyle k_2$ and $\displaystyle k_3$ have different radii. A circle $\displaystyle k_1$ touches both of them from the inside. The circles $\displaystyle k_2$ and $\displaystyle k_3$ are tangent to a circle $\displaystyle k_4$ from the inside. Show that the radical axis of $\displaystyle k_1$ and $\displaystyle k_4$ passes through the external point of similitude of $\displaystyle k_2$ és $\displaystyle k_3$.

(6 pont)

Deadline expired on April 10, 2015.

### Statistics:

 15 students sent a solution. 6 points: Cseh Kristóf, Csépai András, Fekete Panna, Nagy-György Pál, Polgár Márton, Porupsánszki István, Schrettner Bálint, Szebellédi Márton, Szőke Tamás, Williams Kada. 5 points: Lajkó Kálmán. 2 points: 1 student. 1 point: 3 students.

Problems in Mathematics of KöMaL, March 2015