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" The angle formed by a tangent to a circle, and a chord drawn from the point of contact, is equal to the angle in the alternate segment. "
A Course of Mathematics: For the Use of Academies as Well as Private Tuition - Page 294
by Charles Hutton - 1812
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 426 pages
...angles are equal, they are right angles (I. def. 10). Proposition 32. — Theorem. The angles contained by a tangent to a circle and a chord drawn from the point of contact are equal to the angles in the alternate segments of the circle. Let EF be a tangent to the circle...
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The Elementary Geometry of the Right Line and Circle ... With Exercises

William Alexander Willock - Circle - 1875 - 172 pages
...circle, and is tlte tangent, as stateil. 16. The Angle between a Tangent to a circle and a Chord through the point of contact is equal to the angle in the alternate segment. Let AM be the tangent at A in the circle R, and AB the chord, making any angle, a, with AM, and also...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Plane - 1876 - 58 pages
...of these statements follow by the Rule of Conversion. THEOR. 19. Each angle contained by a tangent and a chord drawn from the point of contact is equal to the angle in the alternate segment of the circle. [Euclid's proof] THEOR. 20. Two tangents and two only can be drawn to a circle from...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 pages
...angles are equal, they are right angles (I. def. 10). Proposition 32. — Theorem. The angles contained by a tangent to a circle and a chord drawn from the point of contact are equal to the angles in the alternate segments of the circle. Let EF be a tangent to the circle...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...Therefore, С A is perpendicular to D A. THEOREM XXXVII. The angle contained by a tangent and a chord from the point of contact is equal to the angle in the opposite segment. Let AD be the tangent, and А С the chord ; let AB be the diameter through A, and...
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Elementary geometry

James Maurice Wilson - 1878
...these statements follow by the Rule of Conversion. THEOREM 19. . Each angle contained by a tangent and a chord drawn from the point of contact is equal to the angle in the alternate segment of the circle*. Part. En. Let DBC be a tangent to the circle A at the point B, and let BE be a line...
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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...half the difference of the arcs AC and EF. PROPOSITION XV.—THEOREM. The angle formed by a tangent and a chord drawn from the point of contact is equal to the angle inscribed in the alternate segment of the circle. Let AB be a tangent and EC a chord, forming the angle...
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The Civil-engineer & Surveyor's Manual

Michael McDermott - Civil engineering - 1879 - 586 pages
...CL B. 84. By Euclid III. 26, the < BCL = < BLC = < C 0 B. 85. By Euclid III. 32, the angle contained by a tangent to a circle, and a chord drawn from the...contact, is equal to the angle in the alternate segment of the circle ; ie, in fig. 9, the < TBC = < B 0 C = < CA B. This theorem is much used in railway...
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A Synopsis of Elementary Results in Pure and Applied ..., Volume 1, Part 1

George Shoobridge Carr - Mathematics - 1880
...— The angle in a semicircle is a right angle. III. 32. — The angle between a tangent and a chord from the point of contact is equal to the angle in the alternate segment. III. 33 and 34. — To describe or to cut off a segment of a circle which shall contain a given angle....
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Practical geometry for art students

John Carroll (art master.) - Geometry - 1881
...FiJI37 LESSON XXII. — IRREGULAR FIGURES INSCRIBED IN AND DESCRIBED ABOUT THE CIRCLE. " The angles made by a tangent to a circle and a chord drawn from the point of contact are equal to the angles in the alternate segments of the circle." — Eudid iii. 32. Problem 138. —...
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