 | George William Myers - Mathematics - 1910 - 304 pages
...circumference, is called the point of tangency, or the point of contact. PROPOSITION XXX 101. Theorem: A tangent to a circle is perpendicular to the radius drawn to the point of contact; and conversely, a line drawn perpendicular to a radius at its outer end is a tangent to the circle.... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...outside the circle. Therefore XY is tangent to the circle at P, by § 183. QED 185. COROLLARY 1. A tangent to a circle is perpendicular to the radius drawn to the point of contact. For OP is the shortest line from 0 to XY, and is therefore _L to XY (§ 86); that is, XY is _L to OP.... | |
 | Geometry, Plane - 1911 - 192 pages
...of the non-parallel sides of a trapezoid is parallel to the bases, and equal to half their sum. 3. A tangent to a circle is perpendicular to the radius drawn to the point of contact. 4. If any two chords be drawn through a fixed point within a circle the product of the segments of... | |
 | John Gale Hun, Charles Ranald MacInnes - Trigonometry - 1911 - 234 pages
...these circles at A. Then by definition the spherical angle is measured by the angle TAS. But since a tangent to a circle is perpendicular to the radius drawn to the point of contact, AT and AS are perpendicular to OA, and hence TAS is the measure of the diedral angle T-OA-S or B-OA-C.... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...and therefore AB is tangent to the circle at C. (Definition of a tangent, § 66.) 271. COROLLARY 1. A tangent to a circle is perpendicular to the radius drawn to the point of contact. For OC is the shortest line from 0 to AB, and is therefore -L to AB. 272. COROLLARY 2. A perpendicular... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...and therefore AB is tangent to the circle at C. (Definition of a tangent, § 66.) 271. COROLLARY 1. A tangent to a circle is perpendicular to the radius drawn to the point of contact. For 00 is the shortest line from 0 to AB, and is therefore -l. to AB. 272. COROLLARY 2. A perpendicular... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 230 pages
...chords are unequally distant from the center, the chord at the less distance is the greater. 313. A tangent to a circle is perpendicular to the radius drawn to the point of tangency. 314. A straight line perpendicular to a radius at its outer extremity is tangent to the circle.... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...center of the circle to a side of an inscribed square. (See § 308.") PROPOSITION X. THEOREM 313. A tangent to a circle is perpendicular to the radius drawn to the point oftangency. AMTB Given line AB, tangent to circle 0 at T, and OT, a radius drawn to the point of tangency.... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...is, no point of AB except E lies on the circle. Whence AB is a tangent. § 114 116. Corollary 1. A tangent to a circle is perpendicular to the radius drawn to the point of contact. [Note that we know that OE < OD. Then apply § 77.] 117. Corollary 2. A perpendicular to a tangent... | |
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A tangent to a circle is perpendicular to the radius drawn to the point of contact. 
