<content> <p>g</p> </content>

a1eec082-0233-4140-9334-aa3e39e27e1b 167 Alvaro Diaz Falconi 4 5 false false false 0 0 decimal

Elementary triangle geometry

z# RE z# z# Conjugate + 2 / 11 line :

z# IM z# z# Conjugate - 2 i * / 11 line :

a b i * + RE a

a b i * + Re a b i * + Re

M# z2xy A# 0 : r# 0 : 12 mat a# M# sys2mat.1 r# r# 1 + : A# r# 1 el a# RE : A# r# 2 el a# IM : 13 mat for A# 31 line :

A# xy2z A# 1 el i A# 2 el * + 11 line :

Line A# B# gL R# A# IM B# IM - (z RE * A# RE B# RE - (z IM * - A# RE B# IM * A# IM B# RE * - (+ numden : R# 1 el R# 2 el * 21 line :

Intersection a# b# g∩ a# b# 21 mat x y 21 mat roots xy2z 11 line :

At x# A# g\0040\ x# x A# RE ≡ y A# IM ≡ 21 sys at 11 line :

Paralel at A to a a# A# g\007C\ a# a# A# g\0040\ - 11 line :

Parpendicular at A to a a# A# g⟂ a# i z * g\0040\ A# g\007C\ 11 line :

∥

Signed distance r# A# gδ r# A# g\0040\ r# x diff (2^r# y diff (2^+ sqrt / 11 line :

Signed bisector r# s# gβ s# x diff 2^s# y diff 2^+ sqrt r# * r# x diff 2^r# y diff 2^+ sqrt s# * + 11 line :

Circle center and radious from 3 points A# B# C# gC eq# x a# - (2^y b# - (2^+ r# 2^- : a# b# r# 31 mat 00031 mat u# f# a# b# r# 13 mat u# 1 el u# 2 el u# 3 el 13 mat : eq# A# g\0040\ eq# B# g\0040\ eq# C# g\0040\ 31 mat 21 line : al_nleqsolve : a# i b# * + r# 12 mat 31 line :

XYPlot shorthands S# A# B# gXY S# Circle ≡ circle A# Re A# Im B# 13 mat transpose 11 mat blue solid stack 11 mat 11 mat S# Point ≡ A# str2num z2xy B# 8 blue augment eval A# str2num z2xy A# 10 blue augment eval 21 sys S# Poly ≡ polygon A# str2num vectorize z2xy 11 mat # B# 4 substr concat solid 2 B# stack 11 mat 11 mat A# str2num vectorize z2xy A# transpose 10 black augment eval 21 sys Nothing else if 11 line :

Problem: construct a triangle from an angle A, its bisector line h and the opposite side. angle A (BAC) 40 degrees, opposite side a (BC) 4 cm and angle A's bisector h (AD) 3 cm

Ref: https://en.smath.com/forum/yaf_postst25461findunread_roots-function.aspx

z x i y * + :

clr #2F0FF004 :

α 40 deg * : x.B 2 - : h 3 : 31 sys

Angle A
Point B
bisector length

B x.B 0 i * + : C x.B - 0 i * + : E 0 : 31 sys

Π Point E . gXY μ.B B C gL E g⟂ : tg.B α - tan x x.B - (* y - : ptg.B tg.B B g⟂ : O μ.B ptg.B g∩ : Point O . gXY 21 line x y Arc.O O z - abs O B - abs - : F 0 i 0 y Arc.O y roots * + : Point F . gXY 21 line D E F - abs x.A * E F - abs y.A + / 0 i * + : x.A y.A 21 mat x.A i y.A * + D - abs h - x.A y.A Arc.O 21 mat 2221 mat Broyden : A x.A i y.A * + eval : Poly A B C 13 mat clr gXY 41 line Point D . gXY x y h A C gL A B gL gβ : 101 sys :

A 3.085 1.9784 i * +

A D - abs 3

F 0.7279 i * -

D 0.8298

Alvaro

4 appVersion 1.2.9018.0