 | Benjamin Peirce - Geometry - 1837 - 216 pages
...therefore, by art. 11, the same direction with the circumference at M. 120. Theorem. The tangent to a circle is perpendicular to the radius drawn to the point of contact. Demonstration. The radius OM = ON (fig. 58) is shorter than any other line, as OP, which can be drawn... | |
 | X. Y. Z. - Equations - 1843 - 124 pages
...Angle at the centre is double the Angle at the Circumference. (Euclid 20, 3.) - - 90 6*. A Tangent to a Circle is perpendicular to the Radius drawn to the Point of Contact. (Euclid, 3, 16.) - - ib. 7*. If two Tangents be drawn at the extremity of a Chord to intersect, the... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...perpendicular to a radius at its extremity is a tangent to the circle. Conversely. Every tangent to a circle is perpendicular to the radius drawn to the point of contact. 1st. Let AB be perpen- F>s' ^ DE dicular to the radius CD, at its extremity D ; then we have to prove... | |
 | Nathan Scholfield - 1845 - 894 pages
...PROPOSITION IX. THKOREMt A perpendicular at the extremity of a radius is a tangent of the circumference ; and conversely, a tangent to the circle is perpendicular to the radius drawn to the point of contact. Let ABD be perpendicular to the radius CB, it shall touch the circle in the point B. For to show that... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...circumference in only one point : it is therefore tangent to it at the point D (D. 8). Therefore, etc. Cor. Conversely. — A tangent to the circle is perpendicular...to the tangent, is perpendicular to the tangent at D (BI Th. XIV.) Therefore, etc. THEOREM V. Two parallel lines intercept equal arcs on the circumference.... | |
 | E. M. Reynolds - Geometry - 1868 - 172 pages
...A. Hence every other point in AB except A lies without the circumference. Conversely. Every tangent is perpendicular to the radius drawn to the point of contact. For the radius OA is the shortest line that can be drawn to AB ; it is therefore perpendicular to it. COR.... | |
 | George Holmes Howison - Geometry, Analytic - 1869 - 622 pages
...course, must accept upon authority the meaning of the equations employed. To prove [hat the tangent to a circle is perpendicular to the radius drawn to the point of contact. — Let the axes be rectangular, and the center of the circle at the origin. Its equation is, in that... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...sphere, and is consequently tangent to the sphere. 44. Corollary. Conversely, a plane tangent to a sphere is perpendicular to the radius drawn to the point of contact. For, since every point of the plane except the point of contact is without the sphere, the radius drawn... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...sphere, and is consequently tangent to the sphere. 44. Corollary. Conversely, a plane tangent to a sphere is perpendicular to the radius drawn to the point of contact. For, since every point of the plane except the point of contact is without the sphere, the radius drawn... | |
 | Harvard University - 1873 - 732 pages
...two sides of a triangle proportionally is parallel to the third side. 7. Prove that a tangent to a circle is perpendicular to the radius drawn to the point of contact. 8. Prove that parallel chords intercept upon the circumference equal arcs. ANCIENT HISTORY AND GEOGRAPHY.... | |
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A tangent to a circle is perpendicular to the radius drawn to the point of contact. 
