Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 67
... point . And since P represents two points we would have the absurdity of a line cutting a circle in three points . ( 94 ° ) Def . 2. - The point where P and Q meet is called the point of contact . Being formed by the union of two points ...
... point . And since P represents two points we would have the absurdity of a line cutting a circle in three points . ( 94 ° ) Def . 2. - The point where P and Q meet is called the point of contact . Being formed by the union of two points ...
Page 68
... point on a circle are perpendicular to one another . ଓ T P S L ' is a centre - line and Ta tan- gent , both to the point ... contact are respectively equal to the angles in the opposite arcs into which the chord divides the circle . TP is a ...
... point on a circle are perpendicular to one another . ଓ T P S L ' is a centre - line and Ta tan- gent , both to the point ... contact are respectively equal to the angles in the opposite arcs into which the chord divides the circle . TP is a ...
Page 69
... points , two circles can be made to pass through the same three points . But this is not true . ( 96 ° ) .. two circles can intersect in only two points . Cor . Two circles can touch in only one point . For a point of contact is ...
... points , two circles can be made to pass through the same three points . But this is not true . ( 96 ° ) .. two circles can intersect in only two points . Cor . Two circles can touch in only one point . For a point of contact is ...
Page 70
... contact . ( d ) When the distance between the centres is less than the difference of the radii , the greater circle ... point without a circle two tangents can be drawn to the circle . A B S P - Proof . Let S be the and P the point ...
... contact . ( d ) When the distance between the centres is less than the difference of the radii , the greater circle ... point without a circle two tangents can be drawn to the circle . A B S P - Proof . Let S be the and P the point ...
Page 71
... point without S and its radius the tangent from the point to the circle S. 116 ° . The following examples furnish ... contact are concyclic . Let A , B , C , D be the centres of the circles , and P , Q , R , S be the points of contact ...
... point without S and its radius the tangent from the point to the circle S. 116 ° . The following examples furnish ... contact are concyclic . Let A , B , C , D be the centres of the circles , and P , Q , R , S be the points of contact ...
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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