Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 43
... constant , we deduce the following— I. When two angles of a triangle are given the third is given also ; so that the giving of the third furnishes no new information . 2. As two parts of a triangle are not sufficient to deter- mine it ...
... constant , we deduce the following— I. When two angles of a triangle are given the third is given also ; so that the giving of the third furnishes no new information . 2. As two parts of a triangle are not sufficient to deter- mine it ...
Page 53
... constant distance from a fixed point in the plane . The compasses , whatever be their form , furnish us with two points , A and B , which , from the rigidity of the instrument , are supposed to preserve an unvarying distance B A A B ...
... constant distance from a fixed point in the plane . The compasses , whatever be their form , furnish us with two points , A and B , which , from the rigidity of the instrument , are supposed to preserve an unvarying distance B A A B ...
Page 64
... constant . ( 105 ° , 4 ) Cor . 2. Since and LAPBLAOB minor , LAQB LAOB major , ( 37 ° ) LAPB + LAQB = a straight angle . and LAOB minor + LAOB major = 4 right angles ... And APBQ is a concyclic quadrangle . Hence a concyclic quadrangle ...
... constant . ( 105 ° , 4 ) Cor . 2. Since and LAPBLAOB minor , LAQB LAOB major , ( 37 ° ) LAPB + LAQB = a straight angle . and LAOB minor + LAOB major = 4 right angles ... And APBQ is a concyclic quadrangle . Hence a concyclic quadrangle ...
Page 65
... constant and its vertical angle APC constant . Therefore the locus of the vertex of a triangle which has a constant base and a constant vertical angle is an arc of a circle passing through the end - points of the base . This property is ...
... constant and its vertical angle APC constant . Therefore the locus of the vertex of a triangle which has a constant base and a constant vertical angle is an arc of a circle passing through the end - points of the base . This property is ...
Page 75
... constant length . Find the locus of the middle point of AB . 24. Two equal circles , touch one another and each touches one of a pair of perpendicular lines . What is the locus of the point of contact of the circles ? 25. Two lines ...
... constant length . Find the locus of the middle point of AB . 24. Two equal circles , touch one another and each touches one of a pair of perpendicular lines . What is the locus of the point of contact of the circles ? 25. Two lines ...
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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