<content> <p>g - real valued coordinates</p> </content>

a1eec082-0233-4140-9334-aa3e39e27e1b 203 Alvaro Diaz Falconi 4 5 false false false 0 0 decimal

Elementary triangle geometry

As# str2xy x. y. 12 mat As# num2str concat str2num vectorize 11 line :

As# gPoint As# str2xy o augment eval As# str2xy As# num2str augment eval 21 sys 11 line :

r# gLine x y r# r# : big - y r# IsDefined num2str 1 ≡ big - big - y r# y roots big big y r# y roots 22 mat eval x big - r# x roots big - x big r# x roots big 22 mat eval if 21 line :

As# Bs# gLine A# B# 12 mat As# str2xy Bs# str2xy 12 mat eval : A# 1 el A# 2 el 1 B# 1 el B# 2 el 1 x y 133 mat det gLine 21 line :

Os# R# gCircle t# 03601 range deg * : O# Os# str2xy : 12 mat R# t# cos vectorize * O# 1 el + R# t# sin vectorize * O# 2 el + augment eval 21 line :

As# Bs# Cs# gTriangle As# str2xy Bs# str2xy Cs# str2xy As# str2xy stack As# gPoint Bs# gPoint Cs# gPoint 41 sys eval 11 line :

As# Bs# δ A# B# 12 mat As# str2xy Bs# str2xy 12 mat : A# 1 el B# 1 el - (2^A# 2 el B# 2 el - (2^+ sqrt 21 line :

A# B# transpose * 111 mat * sqrt

big 100 :

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

α 40 deg * : x.B y.B 12 mat 2 - 012 mat : h 3 : 31 sys

Angle A
Point B
bisector length

x.C y.C 12 mat x.B - y.B 12 mat : x.E y.E 12 mat 0012 mat : x.Z y.Z 12 mat x y 12 mat : 31 sys

Π μ.E x 0 y * - : μ.E gLine 21 line tg.B α - tan x x.B - (* y - : tg.B gLine 21 line ptg.B 1 α tan / x x.B - (* y - : ptg.B gLine 21 line x.O y.O 21 mat μ.E ptg.B 21 mat x y 21 mat roots : O gPoint 21 line x y C.O O Z δ 2^O B δ 2^- : O O B δ gCircle 21 line x.F y.F 21 mat x.E x.E y C.O y roots 21 mat : 11 line x.D y.D 21 mat E F δ x.A * E F δ y.A + / 021 mat : x.A y.A 21 mat A D δ h - x.A y.A C.O 21 mat x.A y.A 21 mat 2221 mat roots : A D gLine 31 line E F D gTriangle A B C gTriangle 91 sys :

x.A y.A 21 mat 3.085 1.9784 21 mat

A D δ 3

y.A y.D - x.A x.D - atan deg 41.26

Alvaro

4 appVersion 1.2.9018.0