Intermediate Geometry: Being Sections V and VI of "geometry, Theoretical and Practical".W.B. Clive, University Tutorial Press Ld., 1908 - Geometry |
From inside the book
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Page 411
... chord PQ of the outer circle touches the inner circle at R. Show that = OP : 00 PR : RQ . 8. If O is the in - centre of ABC , and AO meets BC in D , prove that AO : OD = AB + AC : BC . 9. If in a quadrilateral the bisectors of one pair ...
... chord PQ of the outer circle touches the inner circle at R. Show that = OP : 00 PR : RQ . 8. If O is the in - centre of ABC , and AO meets BC in D , prove that AO : OD = AB + AC : BC . 9. If in a quadrilateral the bisectors of one pair ...
Page 414
... chords PAB , PCD are drawn to meet the circle in A , B , C , D. PEF bisects APC , and meets the chord AC in E , and the chord BD in F ; prove that BF : FD = CE : EA . 7. Trisect a given straight line by means of Theorem T.12 . 8. Draw ...
... chords PAB , PCD are drawn to meet the circle in A , B , C , D. PEF bisects APC , and meets the chord AC in E , and the chord BD in F ; prove that BF : FD = CE : EA . 7. Trisect a given straight line by means of Theorem T.12 . 8. Draw ...
Page 422
... chord parallel to the tangent at A to a circle , and a line AD meets BC in E and the circle in D ; prove that AE : AB = AB : AD . 13. ABCD is a parallelogram , and P and Q are any two points in AD and CD . PM , QN are any two parallel ...
... chord parallel to the tangent at A to a circle , and a line AD meets BC in E and the circle in D ; prove that AE : AB = AB : AD . 13. ABCD is a parallelogram , and P and Q are any two points in AD and CD . PM , QN are any two parallel ...
Page 423
... chord . 17. ABC is a triangle right - angled at A ; a point D is taken in the hypotenuse BC such that CB : BA = BA ... chords are in a given ratio . 21. From a given point on the circumference of a circle draw two chords which are in a ...
... chord . 17. ABC is a triangle right - angled at A ; a point D is taken in the hypotenuse BC such that CB : BA = BA ... chords are in a given ratio . 21. From a given point on the circumference of a circle draw two chords which are in a ...
Page 443
... chords of a circle which intersect in 0 . Prove that △ AOB : COD = sq . on OA : sq . on OD . 4. Similar triangles are to one another in the ratio of the squares of ( 1 ) corresponding medians , ( 2 ) the radii of their inscribed ...
... chords of a circle which intersect in 0 . Prove that △ AOB : COD = sq . on OA : sq . on OD . 4. Similar triangles are to one another in the ratio of the squares of ( 1 ) corresponding medians , ( 2 ) the radii of their inscribed ...
Other editions - View all
Intermediate Geometry: Being Sections V and VI of Geometry, Theoretical and ... Walter Percy Workman No preview available - 2023 |
Intermediate Geometry: Being Sections V and VI of Geometry, Theoretical and ... Walter Percy Workman No preview available - 2023 |
Intermediate Geometry: Being Sections V and VI of Geometry, Theoretical and ... Walter Percy Workman No preview available - 2019 |
Common terms and phrases
ABCD B.Sc base bisects centre of similitude Ceva's Theorem CHAPTER chord circles touch circumcircle collinear concurrent concyclic points Cons Cons.-Draw cyclic quadrilateral diagonals diameter dihedral angle divided equiangular EXERCISES externally figure Find the locus Geometry given circles given line given point given ratio given straight line harmonic range Hence hypotenuse intersecting planes irrational numbers LAOB LDPE lies in plane line drawn line joining line perpendicular mean proportional meet nine-point circle opposite edges orthocentre pair parallel planes parallelogram parallelopiped perpendicular Picture Plane plane X plane XX polygon Proof quadrilateral radical axis radii radius rational numbers rectangle contained remaining Theorems Required to prove respectively right angles segments similar triangles Similarly solid angle square tangents tetrahedron THEOREM.-If three lines triangle ABC Tutorial vertex vertical angle
Popular passages
Page 570 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 584 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Page 575 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 424 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Page 10 - The historical part is concise and clear, but the criticism is even more valuable, and a number of illustrative extracts contribute a most useful feature to the volume.
Page 571 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 16 - The object of the UNIVERSITY TUTORIAL SERIES is to provide candidates for examinations and learners generally with text-books which shall convey in the simplest form sound instruction in accordance with the latest results of scholarship and scientific research. Important points are fully and clearly treated, and care has been taken not to introduce details which are likely to perplex the beginner. The Publisher will be happy to entertain applications from Schoolmasters for specimen copies of any...
Page 583 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means...
Page 574 - If a parallelogram and a triangle be on the same base and between the same parallels, the parallelogram shall be double of the triangle.
Page 574 - Equal triangles, on equal bases, in the same straight line, and on the same side of it, are between the same parallels. Let...