 | William Chauvenet - Geometry - 1887 - 346 pages
...line cannot intersect a circle in more than two points. PROPOSITION IX. A straight line tangent to a circle is perpendicular to the radius drawn to the point of contact. Corollary I. A perpendicular to a tangent line drawn through the point of contact must pass through... | |
 | Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...only one tangent can drawn to a circle at a given point on the circumference. COR. 2. Any tangent to a circle is perpendicular to the radius drawn to the point of contact. COR. 3. The centre of a circle lies in the perpendicular to any tangent at the point of contact. For... | |
 | William Elwood Byerly - 1888 - 284 pages
...infinitesimal arcs, are straight lines, and PAP 1 and P'BP are right angles, since the tangent to a circle is perpendicular to the radius drawn to the point of contact. F'P+PF=F'P'+P'F, by the definition of an ellipse. Take away from the first sum F'P + BF, and we have... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...the circle, and therefore MB is a tangent to the circle at A. § 213 QED 240. .CoR. 1. A tangent to a circle is perpendicular to the radius drawn to the point of contact. For, if MB is tangent to the circle at A, every point of MB, except A, is without the circle. Hence,... | |
 | Education - 1896 - 446 pages
...polygon consist when each of its angles contains 150 degrees? Explain. 5. Prove that a line tangent to a circle is perpendicular to the radius drawn to the point of contact. 6. Prove the area of a rectangle is equal to the product of its base by its altitude. How would you... | |
 | Euclid - Geometry - 1892 - 460 pages
...intersection coincide. 1. To prove by the Method of Limits that a tangent to a cirri? is at right angles to the radius drawn to the point of contact. Let ABD be a circle, whose centre is C ; and PA BQ a secant cutting the C" in A and B ; and let P'AQ' be the limiting... | |
 | William Chauvenet - 1893 - 340 pages
...be unequal, by Proposition XXL, Book I. PROPOSITION IX.—THEOREM. 23. A straight line tangent to a circle is perpendicular to the radius drawn to the point of contact. For any other point of the tangent, as D, must lie outside of the circle, and therefore the line OD,... | |
 | Webster Wells - Geometry - 1894 - 256 pages
...tangent to the circle. (§ 149.) PROPOSITION XV. THEOREM. 170. (Converse of Prop. XIV.) A tangent to a circle is perpendicular to the radius drawn to the point of contact. ACS To prove that AB is perpendicular to the radius OC drawn to the point of contact. If AB is tangent... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...chords that which is at a less distance from the centre is the greater. 181. Theorem. A tangent to a circle is perpendicular to the radius drawn to the point of contact. 182. Theorem. A perpendicular to a radius at its end is a tangent to the circle. 183. Theorem. A perpendicular... | |
 | Webster Wells - 1894 - 172 pages
...is tangent to the sphere. (§ 579.) 596. COR. (Converse of Prop. VIII.) A plane tangent to a sphere is perpendicular to the radius drawn to the point of contact. Let the plane MN be tangent to the sphere AC. To prove that MN is perpendicular to the radius OA drawn... | |
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A tangent to a circle is perpendicular to the radius drawn to the point of contact. 
