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
Deadline expired on November 12, 2012.
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.