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From:**Seiichi Kirikami**

Date: Thu, Jan 9, 2014 at 11:16 AM

Subject: [EGML] Numerical computation of the coordinates of the points concerning Morley Triangle [2 Attachments]

To: Anopolis@yahoogroups.com[Attachment(s) from seiichi kirikami included below]Dear friends,

Given a triangle ABC, we trisect its angles A, B, C and their complementary angles equally. We denote the intersection of equal trisection outside ABC and nearest to BC by Da, the intersection of equal trisection inside the sector of A, outside ABC and nearest to CA by Db and the intersection of equal trisection inside the sector of A, outside ABC and nearest to AB by Dc. Others are defined cyclically. We have 4 equilateral triangles DaDbDc, EaEbEc, FaFbFc and DaEbFc. We denote the the intersections of EaEc and FaFb by G. Others are defined cyclically. We have an equilateral triangle GHI.

See the attached picture.

We obtain the following results from DaEbFc for the triangle {6,9,13}.

(1) Concurrent point of Euler lines AEbFc, BFcDa and CDaEb

Search kx=4.000974899..

(2) Concurrent point of Newton lines AFcDaEb, BDaEbFc and CEbFcDa.

Search kx=2.408489889..

(3) Concurrent point of the lines through centroids of AEbFc and DaBC, BFcDa and EbCA, CDaFb and FcAB.

Search kx=3.573704479..

We obtain the following results from GHI for the triangle {6,9,13}.

(4) Concurrent point of Euler lines AHI, BIG and CGH

Search kx=6.675143096..

(5) Concurrent point of Newton lines AIGH, BGHI and CHIG.

Search kx=11.024402788..

(6) Concurrent point of the lines through centroids of AHI and GBC, BIG and HCA, CGH and IAB.

Search kx=8.416515372..

See the attached MS Excel sheet.

Best regards,

Seiichi

Attachment(s) from seiichi kirikami

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