Victor Oxman, On the Existence of Triangles with Given Circumcircle, Incircle, and One Additional Element,
Forum Geometricorum, 5 (2005) 165--171.

Abstract: We give necesssary and sufficient conditions for the existence of poristic triangles with two given circles  as
circumcircle and incircle, and (1) a side length, (2) the semiperimeter (area),   (3) an altitude, and (4) an angle bisector. We also consider the question of construction of such triangles.

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