Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 4
... diameter is the longest chord in a circle . 3. Parallel lines never meet . 4. Every point equidistant from the end - points of a line- segment is on the right bisector of that segment . SECTION I. THE LINE AND POINT . 9 ° . Space may be ...
... diameter is the longest chord in a circle . 3. Parallel lines never meet . 4. Every point equidistant from the end - points of a line- segment is on the right bisector of that segment . SECTION I. THE LINE AND POINT . 9 ° . Space may be ...
Page 55
... diameter . Where length is not implied , the term diameter is some- times used to denote the centre - line of which it properly forms a part . Thus M is a centre - line and CD is a diameter . 96 ° . Theorem . — Through any three points ...
... diameter . Where length is not implied , the term diameter is some- times used to denote the centre - line of which it properly forms a part . Thus M is a centre - line and CD is a diameter . 96 ° . Theorem . — Through any three points ...
Page 57
... diameters . If AP = PD and CP = PB , then P is the centre . C B Proof . Since P is the middle point of both AD and CB ( hyp . ) , therefore the right bisectors of AD and CB both pass through P. But these right bisectors also pass ...
... diameters . If AP = PD and CP = PB , then P is the centre . C B Proof . Since P is the middle point of both AD and CB ( hyp . ) , therefore the right bisectors of AD and CB both pass through P. But these right bisectors also pass ...
Page 65
... diameter of its circumcircle . ( 88 ° , 3 , Def .; 97 ° , Def . ) Cor . 2. When P moves along the ○ the △ APC ( last figure ) has its base AC constant and its vertical angle APC constant . Therefore the locus of the vertex of a ...
... diameter of its circumcircle . ( 88 ° , 3 , Def .; 97 ° , Def . ) Cor . 2. When P moves along the ○ the △ APC ( last figure ) has its base AC constant and its vertical angle APC constant . Therefore the locus of the vertex of a ...
Page 68
... diameter are parallel . Cor . 2. The perpendicular to a tangent at the point of con- tact is a centre - line . ( Converse of the theorem . ) Cor . 3. The perpendicular to a diameter at its end - point is a tangent . III . Theorem ...
... diameter are parallel . Cor . 2. The perpendicular to a tangent at the point of con- tact is a centre - line . ( Converse of the theorem . ) Cor . 3. The perpendicular to a diameter at its end - point is a tangent . III . Theorem ...
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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