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" The angle between a, tangent and a chord is measured by one-half its intercepted arc. "
Annual catalogue - Page 132
by University of the South - 1896
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Public Documents of Massachusetts, Volume 9

Massachusetts - 1899 - 1234 pages
...other. 3. Prove that in any triangle the greater angle lies opposite the greater side. 4. Prove that the angle between a tangent and a chord is measured by one-half the intercepted arc. 5. Construct a tangent to a circle from a given point without the circle. Explain...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...193.) But, £ arc BDC is a quadraiit. Whence, ZBAC is a right angle. PROPOSITION XXII. THEOREM. 197. The angle between a tangent and a chord is measured by one-half its intercepted arc. JJ Let AE be tangent to the circle BCD at B, and let BC be a chord. • To prove that Z ABC is measured...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...equal circles, the less of two chords is at the greater distance from the centre. 4. An angle formed by a tangent and a chord is measured by one-half its intercepted arc. 5. The diagonals AC and JiD of the quadrilateral ABCD intersect at E. If AE: EC=BE : ED, prove that...
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...extremities to the centre of the circle form a right triangle. CIRCLES PROPOSITION XIII 81 180. Theorem. An angle between a tangent and a chord is measured by one-half its intercepted arc. B D Appl. Cons. Dem. Prove ABC is meas. by £ BC Draw diam. BE to pt. of contact ABE meas. by \ BCE...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...segment less than a semicircle is an obtuse angle. PROPOSITION XIII. THEOREM 205. An angle formed by a tangent and a chord is measured by one-half its intercepted arc. GIVEN — the angle ABC formed by the tangent AB and the chord BC. To PROVE — angle ABC is measured...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 374 pages
...segment less than a semicircle is an obtuse angle. PROPOSITION XIII. THEOREM 197. An angle formed by a tangent and a chord is measured by one-half its intercepted arc. GIVEN— the angle ABC formed by the tangent AB and the chord BC. To PROVE— angle ABC is measured...
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Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 264 pages
...HI. Tfie opposite angles of an inscribed quadrilateral are supplementary. PROP. XXIII. THEOREM. 197. The angle between a, tangent and a chord is measured by one-half its intercepted arc. Given AE a tangent to O BCD at B, and BC a chord. To Prove that Z ABC is measured by £ arc BC. Proof....
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 250 pages
...(§ 193) But since BC is a diameter, 1 arc BDC is a quadrant. PROP. XXII. THKORKM. 197. The aiu/le between a tangent and a chord is measured, by one-half its intercepted arc. -E Given AE a tangent to O BCD at B, and BC a chord. To Prove that Z ABC is measured by £ arc BC....
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...Z CAB is measured by one-half (BC + DE). See (80). PROPOSITION X. THEOREM. 179. An angle formed by a tangent and a chord is measured by one-half its intercepted arc. Let AE be tangent to the circumference BCD at B, and let BC be a chord. At B erect a perpendicular;...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...inscribed quadrilateral are supplementary. PLANE GEOMETRY. — BOOK II. PROP. XXIII. THEOREM. 197. The angle between a tangent and a chord is measured by one-half its intercepted arc. B -E Given AE a tangent to O BCD at B, and BC a chord. To Prove that Z ABC is measured by | arc BC....
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