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	(10 students).
5 points:	Lajkó Kálmán	(1 student).
2 points:	1 student.
1 point:	3 students.

Problems in Mathematics of KöMaL, March 2015