X(999): "X(999) is the radical center of the mixtilinear incircles."
偽旁切圓
與AB、AC延長線相切且與外接圓外切
與AB、AC的切點連線中點為A-旁心
X(55)
X(6244): "X(6244) = radical center of mixtilinear excircles"
偽外接圓
過B、C且與內切圓內切
與內切圓的切點在連接A-旁心JA和內切圓在BC的切點D的直線上；過JAD的中點
X(479): "Let A′ be the point in which the incircle is tangent to a circle that passes through vertices B and C, and define B and C cyclically. The lines AA′, BB′, CC′ concur in X(479)."
X(57): "Let Oa be the circle passing through B and C, and tangent to the incircle. Define Ob and Oc cyclically. Let A′ be the point of tangency of Oa and the incircle, and define B′ and C′ cyclically. Triangle A′B′C′ is perspective to the intouch triangle at X(57). Also, X(57) is the radical center of circles Oa, Ob, Oc."
偽旁接圓
過B、C且與A-旁切圓內切
與A-旁切圓的切點在連接內心I和A-旁切圓在BC的切點D′的直線上；過ID′的中點
X(5423): "Let A′ be the point in which the A-excircle is tangent to the circle OA that passes through vertices B and C, and define B′ and C′ cyclically. The lines AA′, BB′, CC′ concur in X(5423)."
