 | Franklin Ibach - Geometry - 1882 - 208 pages
...COR. 4. — Any angle inscribed in a segment greater than a semicircle is acute. THEOREM XV. 211. Any angle formed by a tangent and a chord is measured by half the intercepted arc. Let the Z. ABD be formed by the tangent CD and the chord AB. To prom that Z. ABD is... | |
 | Charles Davies - Surveying - 1883 - 614 pages
...then the common tangent point C is in the line BD produced, and the chord CB = CD+BD. The angle OAD, formed by a tangent and a chord, is measured by half the arc ACD ; hence, R sin OAD = R sin IAD = \AD (see Legendrc, Trig. Arts. 64 and 30) ; hence, AD = 2R sin... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...angle DAB is measured by half the arc DCB, the angle DCB by half the arc DAB : hence, the two angles, taken together, are measured by half the circumference : hence, their sum is equal to two right angles. GEOMETRY. PROPOSITION XIX. THEOREM. Any angle formed b1j tiro chords, 1rhich intersect, is measured... | |
 | William Elwood Byerly - 1888 - 284 pages
...— a Since tan v = — tan |, v = JT — | by trigonometry. In the figure (see next page), PTO being formed by a tangent and a chord, is measured by half the arc PT, and therefore is equal to |. PTA, then, is equal to K, and the line PT is a normal. Hence the normal... | |
 | George Albert Wentworth - 1889 - 276 pages
...semicircle is acute, and every angle inscribed in a segment less than a semicircle is obtuse. 103. Theorem. The angle formed by a tangent and a chord is measured by half the intercepted arc. 104. Theorem. An angle which has its vertex within the circle is measured by half... | |
 | George Albert Wentworth - 1889 - 264 pages
...semicircle is acute, and every angle inscribed in a segment less than a semicircle is obtuse. 103. Theorem. The angle formed by a tangent and a chord is measured by half the intercepted arc. 104. Theorem. An angle which has its vertex within the circle is measured by half... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...two secants is measured by half the difference of the included arcs. Proposition XXI. A Theorem. 184. The angle formed by a tangent and a chord is measured by half the intercepted arc. Proposition XXII. A Theorem. 185. An angle formed by two tangents is measured by half... | |
 | William Elwood Byerly - Calculus, Integral - 1895 - 298 pages
...— a Since tann = — tan|, v = it — I by trigonometry. In the figure (see next page), PTO being formed by a tangent and a chord, is measured by half the arc PT, and therefore is equal to £. PTA, then, is equal to v, and the line PT is a normal. Hence the... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...AECD, are supplements of each other. PLANE GEOMETRY.— BOOK III. Th. 12, C. 1. PROPOSITION XIX. — THEOREM. The angle formed by a tangent and a chord is measured by one-half the arc included between its sides. Given.— Let AB be a tangent to a circle EFG at the point... | |
 | Teachers - 1901 - 258 pages
...cither 3 or 4. 3. Prove that the non-parallel sides of an inscribed trapezoid are equal. 4. Prove that the angle formed by a tangent and a chord is measured by one half of the intercepted arc. Take either f, or 6. 5. Find the mean proportional of 4 and 9 —... | |
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BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles. 
