X1339

NAGEL-SCHRÖDER POINT

Let NaNbNc be the extouch triangle of ABC; viz., Na is where the A-excircle meets line BC, and NaNbNc is the pedal triangle of X40. Let I = incenter of ABC. The circles (AIX’), (BIY’), (CIZ’) concur in two points: I and X1339. (Jean-Pierre Ehrmann, Hyacinthos #6545)
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 474 }: Central Line L(1, 474) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_1339 = NAGEL-SCHRÖDER POINT (-0.2381, -0.2333) A B C X1 X474 X1339 (a, b, c) = (5, 6, 7) | AB = 1

X1339 (NAGEL-SCHRÖDER POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b+c-2a)[4bc(b+c-a) - (a+b+c)(b^{2} + c^{2} - a^{2})]/(b+c-3a)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(5.193116504958\)
▸ Incident Central Lines1 line

{1, 474}