- Jul 3, 2014For P = N:[APH](Nna) = the reflection of (Na) in NA)](Na) = the reflection of (N1) in BC(N1) = the reflection of the NPC (N) in AHso Ma is the tangency point. Where:[the congruent circles (Nna) and (N) are tangent,Also for P = N the triangles are perspective.If P = I, then they are, with perspector the circumcenter O.Which is the locus of P such that ABC, MaMbMc are perspective?Similarly Mb, McMa = the midpoint of PPpaPpa = the reflection of Pa in PAPa = the reflection of P1 in BCP1 = the reflection of P in AHDenote:Let ABC be a triangle and P a point.In fact Ppa, Ppb, Ppc are the reflections of the feet ofaltitudes in PA, PB, PC, resp.So the proplem is:Which is the locus of P such that the reflections ofthe altitudes AA',BB',CC' in AP, BP, CP, resp. are concurrent?(I think it was discussed in hyacinthos)APHThe reflections of AH,BH,CH in AN,BN,CN are concurrentat X(252)

Luis González :

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