Problem A. 570. (October 2012)
A. 570. Given a triangle ABC. For an arbitrary interior point X of the triangle denote by A_{1}(X) the point intersection of the lines AX and BC, denote by B_{1}(X) the point intersection of the lines BX and CA, and denote by C_{1}(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 AC_{1}(P)PB_{1}(P), BA_{1}(P)PC_{1}(P) and CB_{1}(P)PA_{1}(P) has an inscribed circle.
Proposed by: G. Holló, Budapest
(5 pont)
Deadline expired on 12 November 2012.
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