Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 74
... regular 12 - sided polygon in a circle . 7. If r , r ' be the radii of two circles , and d the distance between them , the circles touch when d = r ± r . 8. Give the conditions under which two circles have 4 , 3 , 2 , or I common ...
... regular 12 - sided polygon in a circle . 7. If r , r ' be the radii of two circles , and d the distance between them , the circles touch when d = r ± r . 8. Give the conditions under which two circles have 4 , 3 , 2 , or I common ...
Page 86
... REGULAR POLYGONS . 132 ° . Def . I. A closed rectilinear figure without re - entrant angles ( 89 ° , 2 ) is in ... regular polygons . Def . 2. - A regular polygon has its vertices concyclic , and all its sides equal to one another . The ...
... REGULAR POLYGONS . 132 ° . Def . I. A closed rectilinear figure without re - entrant angles ( 89 ° , 2 ) is in ... regular polygons . Def . 2. - A regular polygon has its vertices concyclic , and all its sides equal to one another . The ...
Page 87
... regular polygons expressed in right angles and in degrees are found , by putting proper values for n , to be as follows : - Equilateral triangle , 60 ° Square ,. I 90 ° Pentagon , 108 ° Octagon , Decagon , Dodecagon , · 3135 ° 144 ° 150 ...
... regular polygons expressed in right angles and in degrees are found , by putting proper values for n , to be as follows : - Equilateral triangle , 60 ° Square ,. I 90 ° Pentagon , 108 ° Octagon , Decagon , Dodecagon , · 3135 ° 144 ° 150 ...
Page 88
... regular hexagon . Cor . Since AOB is an equilateral triangle , AB = AO ; .. the side of a regular hexagon is equal to the radius of its circumcircle . 135 ° . Problem . - To determine which species of regular polygons , each taken alone ...
... regular hexagon . Cor . Since AOB is an equilateral triangle , AB = AO ; .. the side of a regular hexagon is equal to the radius of its circumcircle . 135 ° . Problem . - To determine which species of regular polygons , each taken alone ...
Page 90
... regular octagon in a circle . 25. To inscribe a regular dodecagon in a circle . 26. A , B , C , D , are consecutive vertices of a regular octagon , and A , B ' , C ' , D ' , ... , of a regular dodecagon in the same circle . Find the ...
... regular octagon in a circle . 25. To inscribe a regular dodecagon in a circle . 26. A , B , C , D , are consecutive vertices of a regular octagon , and A , B ' , C ' , D ' , ... , of a regular dodecagon in the same circle . Find the ...
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Common terms and phrases
ABCD Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points end-points equal angles equianharmonic equilateral triangle excircles external bisector fixed point geometric given circles given line given point harmonic range Hence hexagram homographic homologous hypothenuse incircle internal angles inverse points isosceles joins LAOB line-segment locus median middle point nine-points circle opposite sides orthogonally pair parallel parallelogram passes pencil perpendicular perspective plane point of contact point of intersection polar reciprocal Proof quadrangle radical axis radical centre radii radius rectangle rectilinear figure regular polygon rhombus right angle right bisector rotation secant similar Similarly square straight angle symbol tangent tensor theorem Theorem.-The three circles transversal vertex vertices