IMO 1976 LL POL31

Into every lateral face of a quadrangular pyramid a circle is

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IMO 1976 LL POL31

Origin: POL

Problem

Into every lateral face of a quadrangular pyramid a circle is inscribed. The circles inscribed into adjacent faces are tangent (have one point in common). Prove that the points of contact of the circles with the base of the pyramid lie on a circle.