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The locus of the incenter of triangle SBC

Source: Vietnam TST 1985 Problem 2

February 5, 2010
geometryincenterperpendicular bisectorgeometry proposed

Problem Statement

Let ABC ABC be a triangle with AB \equal{} AC. A ray Ax Ax is constructed in space such that the three planar angles of the trihedral angle ABCx ABCx at its vertex A A are equal. If a point S S moves on Ax Ax, find the locus of the incenter of triangle SBC SBC.
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