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