Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 4
... EXERCISES . State the contrapositives and the converses of the follow- ing theorems : - I. The sum of two odd numbers is an even number . 2. A diameter is the longest chord in a circle . 3. Parallel lines never meet . 4. Every point ...
... EXERCISES . State the contrapositives and the converses of the follow- ing theorems : - I. The sum of two odd numbers is an even number . 2. A diameter is the longest chord in a circle . 3. Parallel lines never meet . 4. Every point ...
Page 13
... EXERCISES . I. If two segments be in line and have one common end- point , by what name will you call the distance between their other end - points ? 2. Obtain any relation between " the sum and the differ- ence " of two segments and ...
... EXERCISES . I. If two segments be in line and have one common end- point , by what name will you call the distance between their other end - points ? 2. Obtain any relation between " the sum and the differ- ence " of two segments and ...
Page 21
... EXERCISES . 1. Three lines pass through a common point and divide the plane into 6 equal angles . Express the value of each angle in right angles , and in degrees . 2. OA and OB make an angle of 30 ° , how many degrees are there in the ...
... EXERCISES . 1. Three lines pass through a common point and divide the plane into 6 equal angles . Express the value of each angle in right angles , and in degrees . 2. OA and OB make an angle of 30 ° , how many degrees are there in the ...
Page 38
... EXERCISES . 1. How many lines at most are determined by 5 points ? by 6 points ? by 12 points ? 2. How many points at most are determined by 6 lines ? by 12 lines ? 3. How many points are determined by 6 lines , three of which pass ...
... EXERCISES . 1. How many lines at most are determined by 5 points ? by 6 points ? by 12 points ? 2. How many points at most are determined by 6 lines ? by 12 lines ? 3. How many points are determined by 6 lines , three of which pass ...
Page 51
... EXERCISES . I. ABC is a △ , and A ' , B ' , C ' are the vertices of equilateral As described outwards upon the sides BC , CA , and AB respectively . Then AA ' = BB ' = CC ' . ( Use 52 ° . ) 2. Is Ex . I true when the equilateral As are ...
... EXERCISES . I. ABC is a △ , and A ' , B ' , C ' are the vertices of equilateral As described outwards upon the sides BC , CA , and AB respectively . Then AA ' = BB ' = CC ' . ( Use 52 ° . ) 2. Is Ex . I true when the equilateral As are ...
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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