Problem A. 570. (October 2012)

A. 570. Given a triangle ABC. For an arbitrary interior point X of the triangle denote by A₁(X) the point intersection of the lines AX and BC, denote by B₁(X) the point intersection of the lines BX and CA, and denote by C₁(X) the point intersection of the lines CX and AB. Construct such a point P in the interior of the triangle for which each of the quadrilaterals AC₁(P)PB₁(P), BA₁(P)PC₁(P) and CB₁(P)PA₁(P) has an inscribed circle.

Proposed by: G. Holló, Budapest

(5 pont)

Deadline expired on November 12, 2012.

Statistics:

8 students sent a solution.
5 points:	Bodnár Levente, Janzer Olivér, Omer Cerrahoglu, Szabó 789 Barnabás.
3 points:	1 student.
1 point:	1 student.
0 point:	2 students.

Problems in Mathematics of KöMaL, October 2012