## New answers tagged euclidean-geometry

3

Transferring the Addendum to my previous non-answer to a non-answer of its own, as it's beginning to sprawl (and because it actually seems more significant) ...
It happens that $X(4)$, $X(74)$, $X(1138)$ also lie on the circumcubic $K279$, for which there is this geometric description attributed to Angel Montesdeoca:
Let $\triangle A' B' C'$ be the cevian ...

0

Bringing together complex numbers and laziness. Following the answer by @FedorPetrov, we see that $N=(A+B+C)/2$ and so $A'=B+C$. Take inversion with respect to the unit circle (which is just a map $z\mapsto 1/\bar{z}$), then the circles are mapped to the lines connecting $A$ and $BC/(B+C)$ (and two analogous) and we want to prove they intersect at one point. ...

4

Not an answer. I'm just expanding a comment about @PeterTaylor's observation that the known pseudovertices $X(4)$, $X(74)$, $X(1138)$ lie on the Neuberg cubic ...
Bernard Gibert's "Pairs and Triads of points on the Neuberg Cubic
connected with Euler Lines and Brocard Axes Isometric Parallel Chords" Proposition 1 characterizes the Neuberg cubic of $\...

5

This is a report on an unsuccessful computational approach which is rather too long for a comment.
I work with complex numbers to represent the points in the obvious way.
It suffices to consider $\mu(z) = t(z,0,1)$ because this can be extended under the invariants to the full $t(z,z',z'')$. Since multiplication by a complex number is just rotation and ...

Top 50 recent answers are included

#### Related Tags

euclidean-geometry × 440mg.metric-geometry × 243

plane-geometry × 82

reference-request × 40

discrete-geometry × 38

triangles × 37

polygons × 26

elementary-proofs × 25

ho.history-overview × 19

convex-geometry × 19

convex-polytopes × 18

projective-geometry × 17

computational-geometry × 15

real-analysis × 14

ag.algebraic-geometry × 13

dg.differential-geometry × 13

pr.probability × 13

gr.group-theory × 13

co.combinatorics × 12

linear-algebra × 12

nt.number-theory × 11

algorithms × 11

inequalities × 10

terminology × 10

polyhedra × 10