The locus of P such that angle APB is always 40^o is two arcs of a circle with centre O such that angle AOB=80^o and radius equals to the length of OA, excluding the points A and B. To construct the arcs, construct triangle AOB such that angle OAB = angle OBA = 50^o. Taking O as the centre and OA as the radius, you can draw the arcs.

Note: JavaSketchpad cannot support this GSP file. To move P, open the file IT4EMLociFixedAngle.gsp using Geometer's Sketchpad.

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