 | 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... | |
 | 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
...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 —... | |
 | Education - 1922 - 948 pages
...of the chord. In most of the proofs received, the pupil had assumed the theorem which states that an angle formed by a tangent and a chord is measured by half the intercepted arc. But this is the very theorem which is to be proved. Briefly, some of the proofs were:... | |
 | Walter Nelson Bush, John Bernard Clarke - Geometry - 1905 - 378 pages
...measured by i arc ^(7. QED Dem. (3) Both arms on the same side of the diameter through B. QED XII. 2 a. An angle formed by a tangent and a chord is measured by half the intercepted arc. Hyp. If AC and EF intersect at C, and if AC is a chord and EF is a tangent, Cone.... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...measured by half of a semicircumference (?) (249). .-. each is a rt. Z (?) (247). QED 252. THEOREM. The angle formed by a tangent and a chord is measured by half the intercepted arc. Given : Tangent TN ; chord PA ; Z TPA ; arc PA. To Prove : Z TPA is measured by J... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...AGF = Z AHE.] 289 The exterior angle formed by producing a side of PROPOSITION XII. THEOREM 281 An angle formed by a tangent and a chord is measured by half the intercepted arc. HYPOTHESIS. BA is a chord and BT a tangent. CONCLUSION. The ^ ABT is measured by \... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...AGF = Z AHE.] 289 The exterior angle formed by producing a side of PROPOSITION XII. THEOREM 281 An angle formed by a tangent and a chord is measured by half the intercepted arc. HYPOTHESIS. BA is a chord and BT a tangent. CONCLUSION. The Z ABT is measured by J... | |
 | Wisconsin. Department of Public Instruction - Education - 1906 - 124 pages
...measured by one-half its intercepted arc. Cor. An angle inscribed in a semicircle is a right angle. 58. The angle formed by a tangent and a chord is measured by one-half the intercepted arc. 59. The angle formed by two intersecting chords is measured by the half... | |
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The angle formed by a tangent and a chord is measured by half the intercepted arc. 
