| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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