Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 48
... concurrent . Therefore the three medians of a triangle are concurrent . Def . 2.- -The point of concurrence , O , of the medians of a triangle is the centroid of the triangle . Cor . Since O is the middle point of BG , and E is the ...
... concurrent . Therefore the three medians of a triangle are concurrent . Def . 2.- -The point of concurrence , O , of the medians of a triangle is the centroid of the triangle . Cor . Since O is the middle point of BG , and E is the ...
Page 49
... concurrent ( 86 ° ) , therefore the altitudes of the concurrent . ABC are q.e.d. Def . - The point of concurrence of the altitudes of a tri- angle is the orthocentre of the triangle . Cor . 1. If a triangle is acute - angled ( 77 ° , 5 ) ...
... concurrent ( 86 ° ) , therefore the altitudes of the concurrent . ABC are q.e.d. Def . - The point of concurrence of the altitudes of a tri- angle is the orthocentre of the triangle . Cor . 1. If a triangle is acute - angled ( 77 ° , 5 ) ...
Page 85
... three internal bisectors of the angles of a triangle are concurrent . 3 Cor . 2. Since Og is equidistant from L and M , I , passes through O3 . ( 68 ° ) .. the external bisectors of two angles of a triangle CONSTRUCTIVE GEOMETRY . 85.
... three internal bisectors of the angles of a triangle are concurrent . 3 Cor . 2. Since Og is equidistant from L and M , I , passes through O3 . ( 68 ° ) .. the external bisectors of two angles of a triangle CONSTRUCTIVE GEOMETRY . 85.
Page 86
... concurrent . Def . 1. - When three or more points are in line they are said to be collinear . Cor . 3. The line through any two centres passes through a vertex of the ABC . .. any two centres are collinear with a vertex of the . The ...
... concurrent . Def . 1. - When three or more points are in line they are said to be collinear . Cor . 3. The line through any two centres passes through a vertex of the ABC . .. any two centres are collinear with a vertex of the . The ...
Page 98
... concurrent with the diagonals of a parallelogram bisects the parallelogram . 7. The triangle having one of the non - parallel sides of a trapezoid as base and the middle point of the opposite side as vertex is one - half the trapezoid ...
... concurrent with the diagonals of a parallelogram bisects the parallelogram . 7. The triangle having one of the non - parallel sides of a trapezoid as base and the middle point of the opposite side as vertex is one - half the trapezoid ...
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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