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" A tangent to a circle is perpendicular to the radius drawn to the point of contact. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 60
by Nathan Scholfield - 1845
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Elements of Geometry: With Notes

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...
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Elements of Geometry: With Notes

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...
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An Elementary Treatise on Plane and Solid Geometry

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...
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Algebra applied to geometry ... By X. Y. Z.

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...
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Elements of Plane Geometry: For the Use of Schools

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...
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

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...
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A Treatise on Analytic Geometry: Especially as Applied to the Properties of ...

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,...
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Catalogue - Harvard University

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....
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Harvard Examination Papers

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...
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Examination Christmas,1875

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...
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