Geometry with Trigonometry

Index 257

equipollent
point pairs, 185
erected
perpendicular, 44
Euclidean geometry, 61
Euler line, 215
exterior point
circle, 103
exterior region, 30
external bisector, 71

Feuerbach’s theorem, 229
frame of reference, 81
frame reference
orientation, 160
full-angle, 30

geometry
Euclidean, 61
Grassmann supplement, 207

half-angle, 139
half-line, 25
half-lines
opposite, 25
half-plane
closed, 27
open, 26
harmonic mean, 99
harmonic range, 71
hypotenuse, 70

incentre, 206
incircle, 206
indicator
angle, 130
duo-angle, 169
indirect correspondence
natural orders, 90
inequality
triangle, 55
initial point, 25
interior
convex polygon, 76
interior point

circle, 103

interior region, 29

inverse

vector, 191

isogonal conjugates, 234

isometry, 123

isosceles triangle, 51

length, 35

length of radius, 103

line, 21

Cartesian equation, 87

different sides of, 27

one side of, 27

parametric equations, 92

lines

perpendicular, 44

major arc

circle, 114

mean

harmonic, 99

Menelaus’theorem, 195

mid-line

angle-support, 46

mid-point, 38

minor arc

circle, 114

Miquel’s theorem, 232

mobile coordinates, 208

modified sum

angles, 136

mp(A,B),38

multiple radian measures, 249

multiples

angle, 138

Napoleon’s theorem, 219

natural order, 22

natural orders

direct correspondence, 90

naturalorders

indirect correspondence, 90

nine-point circle, 225

non-secant line