 | Harvard University - Geometry - 1899 - 39 pages
...of a quadrilateral is two right angles, the quadrilateral can be inscribed in a circle. THEOREM XVI. An angle formed by a tangent and a chord is measured by one half the intercepted arc. THEOREM XVII. An angle formed by two chords intersecting each other within... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...vertex of a right triangle which has a given hypotenuse as its base. 124 Proposition 129. Theorem. 162. An angle formed by a tangent and a chord is measured by one half the intercepted arc. Hypothesis. AB is tangent to the O FDC at C, and CD is a chord. Conclusion.... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...angle between a tangent and a diameter compare with a right angle ? What is its arc measure ? Theorem. An angle formed by a tangent and a chord is measured by one half the intercepted arc. Data : Any tangent, as EB, and any chord, as AC, forming with EB 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 E, and... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...Case I. Conclusion. 139. Problem XIII. To draw a circle tangent to a given circle. THEOREM XVIII 140. An angle formed by a tangent and a chord is measured by one-half the intercepted arc. Hyp. Let AE be tangent to OC at pt. D, and let DE be a chord of the circle. To... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...arc greater than a semi-circumference ; that is bv an arc greater than a quadrant. THEOREH XLVI. 167. An angle formed by a tangent and a chord is measured by one-half the intercepted arc. Let AE be tangent to the circumference BCD at B, and let BC be a chord. To prove... | |
 | Education - 1904 - 938 pages
...correct. 7. The perpendicular bisector of a chord passes through the center of the circle. Prove. 9. An angle formed by a tangent and a chord is measured by onehalf its intercepted arc. Prove. 10. If from the middle point of the base of a triangle parallel lines to the sides are drawn,... | |
 | George Clinton Shutts - 1905 - 260 pages
...198-202 (1) on measurement, and note their bearing on the theory of proportion. Ex. 165. Prove that an angle formed by a tangent and a chord, is measured by one-half the interccpted arc, using the following construction: Drop a J_ from the center of O O to the chord... | |
 | Education - 1922 - 948 pages
...angle 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... | |
 | 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,... | |
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An angle formed by a tangent and a chord is measured by onehalf the intercepted arc. 
