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" A tangent to a circle is perpendicular to the radius drawn to the point of contact. "
An Elementary Treatise on Plane and Solid Geometry - Page 38
by Benjamin Peirce - 1871 - 150 pages
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Algebra applied to geometry ... By X. Y. Z.

X. Y. Z. - Equations - 1843 - 124 pages
...Circle the 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...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...straight line 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...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...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...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...tangent MD, that is, it will, by 99, coincide with this tangent, which has therefore, by 11, the same direction with the circumference at M. Angles...Theorem. The tangent to a circle is perpendicular to the jadius drawn to the point of contact. Proof. The radius OM = OJV (fig. 58) is shorter than any other...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1865 - 186 pages
...tangent MD, that is, it will, by 99, coincide with this tangent, •vhich has therefore, by ^ 11, the same direction with the circumference at M Angles...drawn to the point of contact. Proof. The radius OM = OJV(fig. 58) is shorter than any other line, as OP, which can be drawn from the point O to the tangent...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1869 - 182 pages
...therefore, by 11, the same direction with the circumference at M Antics formed by Secants and Tnngents. 120. Theorem. The tangent to a circle is perpendicular to the radius drawn to the point of contact. Pronf. The radius OM = OJV(fig. 58) is shorter than any other line, as OP, which can be drawn from...
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 294 pages
...therefore tangent to it at the point D (D. 8). Therefore, etc. Cor. Conversely. — A tangent to the circle is perpendicular to the radius drawn to the point of contact. For any line, as CE, is greater than CF, or its equal CD; hence, CD, being the shortest line from C...
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A Treatise on Analytic Geometry: Especially as Applied to the Properties of ...

George Holmes Howison, Joseph Ray - Geometry, Analytic - 1869 - 574 pages
...beginner, of course, must accept upon authority the meaning of the equations employed. To prove that 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...
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Elementary and Practical Instructions on the Science of Railway Construction

Sir Rowland Macdonald Stephenson - Railroads - 1869 - 262 pages
...circle are derived from geometry, and will be found useful in their application to railway curves. 1 . A tangent to a circle is perpendicular to the radius drawn to the tangent point. Thus the tangent AC is perpendicular to the radius A M. 2. Two tangents drawn to a circle...
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Catalogue - Harvard University

Harvard University - 1873
...which divides 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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