HYACINTHOS 24574

[Antreas P. Hatzipolakis]:

 

Let ABC be a triangle, P a point and A'B'C' the pedal triangle of P.

Denote:

O', Oa, Ob, Oc = the circumcenters of A'B'C', PBC, PCA, PAB, resp.

Which is the locus of P such that the reflections of O'Oa, O'Ob, O'Oc in BC, CA, AB, resp. are concurrent?

H lies on the locus. Point of concurrence = Ο

O lies on the locus. Point of concurrence?

[César Lozada]:

Locus: a degree-13 excentral-circumcurve through O, H

 

Z(O) = cos(2*A)*cos(3*A)-cos(4*A)* cos(B-C) : : (trilinears)

= R^2*X(4)+(7*R^2-2*SW)*X(54)

= midpoint of X(195) and X(2917)

= on lines: (3,8157), (4,54), (49,52), (110,2888), (154,9704), (156,9927), (182,6689), (206,576), (539,10201), (569,6145), (1092,7691), (1147,1154), (1209,6639), (1971,9697), (2904,9707), (3518,7730), (6288,10254), (9813,9827), (10182,10203)

= {X(i),X(j)}-Harmonic conjugate of X(k) for these (i,j,k): (54,3574,578)

= [ -6.005211932220933, 4.58105853930050, 3.240798692647539 ]

 

César Lozada