 | Charles William Hackley - Geometry - 1847 - 248 pages
...tangent, and the tangent must then pass within the circle, which is contrary to definition. Corol. 1. Hence, conversely, a line drawn perpendicular to a...tangent, at the point of contact, passes through the center of the circle ; for there can be but one perpendicular to a given line through a given point.... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...tangent AB, and therefore, CD is perpendicular to AB, (B. I, Prop, xxvi.) Cor. 1. Hence, converse!}', a line drawn perpendicular to a tangent at the point...contact, passes through the centre of the circle. Cor. 2. If two circumferences touch each other either externally or internally; their centres and point... | |
 | Anthony Nesbit - Measurement - 1859 - 494 pages
...5. Any chords in a circle which are equally distant from the centre are equal to each other. 7. An angle formed by a tangent and chord is measured by half the arc of that chord. 8. An angle at the circumference of a circle, is measured by half the arc that subtends it. 9. All... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...the point C to the line AB, and, consequently (th. 21, BI), it is perpendicular to that line. Corol. Hence, conversely, a line drawn perpendicular to a...contact passes through the centre of the circle. THEOREM VIH. • The angle formed by a tangent and chord is measured by half the arc of that chord. Let AB... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...tangent to a circle, it is perpendicular to the radius drawn to the point of contact, and therefore a perpendicular to a tangent at the point of contact passes through the centre of the circle. GEOMETRY. BOOK U. PROPOSITION X. THEOREM. 188. W /ien two circumferences intersect each other, the... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...С С'. A _L to AB, drawn through the point 0, passes through the centres С and С', § 187 (a .L to a tangent at the point of contact passes through the centre of the 0). .'. the line С С', having two points in common with this JL, must coincide with it. .'. 0 is... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...tangent. The radius OK bisects the arc AKB. Therefore AK is equal to KB. PROPOSITION XII.—THEOREM. An angle formed by a tangent and chord is measured by half the arc of that chord. The angle EDB beirig a right angle is measured by half the semi-circumference—that is, by half the... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...of a circle to a tangent will meet it at the point of contact. Also the perpendicular erected upon a tangent at the point of contact passes through the centre of the circle. ELEMENTS OF GEOMETRY. [BOOK H. revolution of AB, the angle and arc continue to increase in the same... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...line С C'. A J_ to A B. drawn through the point 0, passes through the centres С and C', § 187 (a _L to a tangent at the point of contact passes through the centre of the O). .-. the line С С', having two points in common with this _L, must coincide with it. .-. 0 is... | |
 | George Albert Wentworth - Geometry - 1882 - 442 pages
...line C C'. A _L to A B. drawn through the point 0, passes through the centres C and C', § 187 (a _L to a tangent at the point of contact passes through the centre of tl'e O). .'. the line C С", having two points in common with this _L, must coincide with it. .-. 0... | |
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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. 
