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" Hence, conversely, a line drawn perpendicular to a tangent, at the point of contact, passes through the centre of the circle. "
A Course of Mathematics ...: Composed for the Use of the Royal Military ... - Page 297
by Charles Hutton - 1811
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...204. COR. 1. A tangent is perpendicular to the radius drawn to the point of contact. 205. COR. 2. A perpendicular to a tangent at the point of contact passes through the center of the circle. 206. COR. 3. A perpendicular from the center to a tangent meets it at the point...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...shortest Hue from O to XY, and is therefore ± to XY; that is, XY is J. to OP. 186. COROLLARY 2. A perpendicular to a tangent at the point of contact passes through the center of the circle. For a radius is J. to a tangent at the point of contact, and therefore a J_ erected...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...line from 0 to XY, and is therefore _L to XY (§ 86) ; that is, XY is _L to OP. 186. COROLLARY 2. A perpendicular to a tangent at the point of contact passes through the center of the circle. Eor a radius is _L to a ta.nge.nt at the point of contact, and therefore a _L...
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Robbin's New Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...radius.) That is, OA is the shortest line from o to RT. ... OA is i. to RT (87). 204. COROLLARY. The perpendicular to a tangent at the point of contact passes through the center of the circle. (43.) QED PROPOSITION X. THEOREM 205. If two circles are tangent to each other,...
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...point of AB except (7. Show that OD> OC by §151, (8), etc. Write the proof in full. EXERCISES 1. The perpendicular to a tangent at the point of contact passes through the center of the circle. SUGGESTION. — Use indirect proof. Draw the radius to the point of contact....
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...of contact. For OC is the shortest line from O to AB, and is therefore J_ to AB. 272. COROLLARY 2. A perpendicular to a tangent at the point of contact passes through the center of the circle. , For the radius drawn to the point of contact is J. to the tangent, and therefore...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...204. COR. 1. A tangent is perpendicular to the radius drawn to the point of contact. 205. COR. 2. A perpendicular to a tangent at the point of contact passes through the center of the circle. 206. COR. 3. A perpendicular from the center to a tangent meets it at the point...
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Plane Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 344 pages
...distances from the intersection to the points of tangency are equal. TEST FOR DIAMETERS 147. THEOREM 71. A perpendicular to a tangent at the point of contact passes through the center of the circle. FlG. 207 Hypothesis: In QO, AB is tangent to O0 at A and AC _L AB at A. Conclusion:...
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Plane Geometry, with Problems and Application

Herbert Ellsworth Slaught - 1918 - 344 pages
...and therefore E would be inside the circle and AB would not be a tangent. 253. COROLLARY 2. A line perpendicular to a tangent at the point of contact passes through the center of the circle. PLANE GEOMETRY: BOOK II DIAMETER PERPENDICULAR 10 A CHORD 255. THEOREM VI. A...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...and therefore E would be inside the circle and AB would not be a tangent. 253. COROLLARY 2. A line perpendicular to a tangent at the point of contact passes through the center of the circle. PLANE GEOMETRY: BOOK II DIAMETER PERPENDICULAR TO A CHORD 255. THEOREM VI. A...
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