 An angle formed by two chords intersecting within the circumference is measured by one-half the sum of the arcs intercepted between its sides and between the sides of its vertical angle.  Treatise on Elementary Geometry - Page 80by William Chauvenet - 1905Full view - About this book
 | Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...and the figure is a parallelogram. 3. Prove that The angle formed by two chords which cut each other is measured by one-half the sum of the arcs intercepted...sides and between the sides of its vertical angle. ENGLISH. GBAMMAR. 1. Spell the following words (dictated) : Artillery, synonyme, exception, transitive,... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...become a tangent and the intercepted arc has become the arc CNA. PROPOSITION XXIII.— THEOREM. 64. An angle formed by two chords, intersecting within...vertical angle. Let the angle AEC be formed by the chords AH, CD, intersecting within the circumference; then will it be measured by one-half the sum of the... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...FIG. 158. PROPOSITION V. 212. TJteorem. — Any angle formed by two chords intersecting in a circle is measured by one-half the sum of the arcs intercepted between its sides and the sides of its vertical, or opposite, angle. Hi M. — Let the chords AB and CD intersect at P; then... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...F1a. 158. PROPOSITION T. 212. TIteorem. — Any angle formed by two chords intersecting in a circle is measured by one-half the sum of the arcs intercepted between its sides and the sides of its vertical, or opposite, angle. В DEM.— Let the chords AB and CD intersect ai P ;... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...PROPOSITION XVII. THEOREM. The angle formed by two chords which cut each other is measured by one half the sum of the arcs intercepted between its sides and between the sides of its vertical angle. Let AB, CD be two chords which cut each other at E ; then will the angle AED be measured by one half the... | |
 | Universities and colleges - 1879 - 88 pages
...Prove this proposition : The angle formed by two chords which cut each other is measured by one half of the sum of the arcs intercepted between its sides and between the sides of its vertical angle. Latin. [Write only on one Bide of the paper. Number the sheets and write your name at the top of each.... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...BF becomes a tangent; hence CAE = $ AE. QED THEOREM XXII. An angle formed by two intersecting chords is measured by one-half the sum of the arcs intercepted between its sides and the sides of its vertical angle. Let a be an angle formed by the two intersecting chords, AB and CD;... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...quadrant. PROPOSITION III. 193. Theorem.— Any angle formed by two chords intersecting in a circle is measured by one-half the sum of the arcs intercepted between its sides and the sides of its vertical, or opposite, angle. DEMONSTRATION. Let the chords AB and CD (Fig. 91) intersect... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...circumference, how many degrees are there in the angle ABC ? PROPOSITION XX. THEOREM. 208. The angle between two chords, intersecting within the circumference, is measured by one-half the sum of its intercepted arc and the arc intercepted by its vertical angle. In the circle ABC let the chords... | |
 | William Chauvenet - Geometry - 1887 - 336 pages
...perpendicular to AC. Suggestion. Complements of the same argle are equal. PROPOSITION XVI.— THEOREM. 51. An angle formed by two chords, intersecting within...vertical angle. Let the angle AEC be formed by the chord8 AB, CD, intersecting within the circumference ; then will it be measured by one-half the sum... | |
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