| John Radford Young - Euclid's Elements - 1827 - 208 pages
...tangent to the circle, and, conversely, a tangent to a circle is perpendicular to the diameter drawn from **the point of contact. Let ABD be perpendicular to...one which the circle has in common with AD, let CE** be drawn to any other point E in that line, then CE being longer than CB, (Prop.XXII. BI) the point... | |
| John Radford Young - Euclid's Elements - 1827 - 208 pages
...tangent to the circle, and, conversely, a tangent to a circle is perpendicular to the diameter drawn from **the point of contact. Let ABD be perpendicular to...the point B. For to show that this point B is the** ,. BED only one which the circle has in common ~ with AD, let CE be drawn to any other point E in that... | |
| Benjamin Peirce - Geometry - 1837 - 159 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 - 96 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... | |
| Edward Brooks - Geometry - 1868 - 294 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 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 - 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 case,... | |
| Harvard University - 1873
...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.... | |
| 1875 - 164 pages
...proportional to the numbers 2, 4, and 3, and prove the principle involved. 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. XIV. 1. Prove that two triangles... | |
| Education Department,London - 1876
...the circle. If a tangent be defined as the limiting position of a secant, shew that the tangent to a **circle is perpendicular to the radius drawn to the point of contact.** ALGEBRA. SECTION V. Find the difference in value between the arithmetical expression 57 and the algebraical... | |
| |