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" If the distance between the centres of two circles is equal to the difference of their radii, the two circles will touch each other internally. "
SYLLABUS OF PLANE GEOMETRY - Side 34
1876
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1874 - 455 sider
...and greater than their difference (BI, P. VJUL.) ; which was to be proved. PROPOSITION Xm. THEOREM. If the distance between the centres of two circles is equal to the sum of their radii, they win be tangent externally. Let C and D be the centres of two circles, and let the distance between...
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Elementary geometry

James Maurice Wilson - 1878
...will meet in tsvo points. Def, 15. In this case the circles are said to cut one another. OBS. (4). If the distance between the centres of two circles is equal to the difference of their radii, their circumferences will meet in one point only, and one circle will lie...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...circumferences will meet in two points. DEF. 15. In this case the circles are said to cut one another, OBS. (4). If the distance between the centres of two circles is equal to the difference of their radii, their circumferences will meet in one point only, and one circle wifl lie...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 sider
...than the whole ; which is impossible. .'. FG, when produced, must pass through A. QED EXERcfTsES. 1. If the distance between the centres of two circles is equal to the difference of their radii, then the circles must meet in one point, but in no other; that is, they...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - 1896 - 540 sider
...two circles cut each other at right angles they are said to cut orthogonally. l!t. If the square of the distance between the centres of two circles is equal to the sum of the squares of their radii, the circles cut each other orthogonally and conversely. 20. If a circle...
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Examinations Papers

1896
...the straight line which joins their centres, being produced, shall pass through the point of contact. If the distance between the centres of two circles is equal to the difference of their radii, then the circles must meet in one point, but in no other. 2. Inscribe a...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - 1896 - 540 sider
...two circles cut each other at right angles they are said to cut orthogonally. 19. If the square of the distance between the centres of two circles is equal to the sum of the squares of their radii, the circles cut each other orthogonally and conversely. 20. If a circle...
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Bok 1

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 sider
...2. Find the locus of the centres of all circles of given radius, which touch a given circle. \f 3. If the distance between the centres of two circles is equal to 'the sum of their radii, then the circles meet in one point, but in no other ; that is, they touch one another. \/ 4. If two...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - 1901 - 440 sider
...two circles is equal to the sum of their radii, the two circles must touch each other externally. 3. If the distance between the centres of two circles is equal to the difference of their radii, the two circles must touch each other internally. PROPOSITION XIX 209. To...
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A Text-book of Euclid's Elements for the Use of Schools, Bok 1

Euclid - 1904 - 456 sider
...point. 2. Find the locus of the centres of all circles of given radius, which touch a given circle. 3. If the distance between the centres of two circles is equal to the sum of their radii, then the circles meet in one point, but in no other ; that is, they touch one another. 184 PROPOSITION...
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