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" The angle formed by a tangent to a circle, and a chord drawn from the point of contact, is equal to the angle in the alternate segment. "
A Course of Mathematics: For the Use of Academies as Well as Private Tuition - Page 294
by Charles Hutton - 1812
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...of these statements follow by the Rule of Conversion. THEOR. 19. Each angle contained by a tangent and a chord drawn from the point of contact is equal to the angle in the alternate segment of the circle. [Euclid's proof.] THEOR. 20. Two tangents and two only can be drawn to a circle from...
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The Eclectic School Geometry: A Revision of Evan's School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...whole angle CBF is measured by half the whole arc BDF. THEOREM XXXVI. Each angle contained by a tangent and a chord drawn from the point of contact is equal to the angle in the alternate segment. How is APD measured ? How ANP? What is the inference ? Prove that APC is equal to ASP. Cor.—Prove...
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Annual Report of the Chief Superintendent of Education

1885
...debt. I. [13] GEOMETRY. Time, 1 hr. 30 m. 1. Prove that the angle contained by a tangent and a chord from the point of contact is equal to the angle in the opposition segment. 2. On a given straight line, describe a segement the inscribed angle of which shall...
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A Synopsis of Elementary Results in Pure Mathematics: Containing ...

George Shoobridge Carr - Handbooks, vade-mecums, etc - 1886 - 1040 pages
...— The angle in a semicircle is a right angle. III. 32. — The angle between a tangent and a chord from the point of contact is equal to the angle in the alternate segment. III. 33 and 34. — To describe or to cut «ff a segment of a circle which shall contain a given angle....
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...coincidence of the two points which approach one another. PROPOSITION. Each angle contained by a tangent and a chord drawn from the point of contact is equal to the angle in the alternate segment of the circle. [III. 33. Let EBB'F be the secant of© ABB'D through B,B', and BD any other chd. through...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Plane - 1891 - 406 pages
...intercepted arcs. PROP. II. An inscribed angle is measured by half of its intercepted arc. PROP. III. An angle formed by a tangent to a circle and a chord drawn to the point of contact is measured by half of the intercepted arc. PROP. IV. In any circle, angles...
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Euclid's Elements of Geometry, Books 1-6

Henry Martyn Taylor - 1893 - 504 pages
...Circles, which have a common tangent at a point, touch each other. 7. Prove that the angle between a tangent to a circle and a chord drawn from the point of contact is half of the angle subtended at the centre by the chord. A straight line which cuts a circle is often...
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The Student's Guide to Accountancy

Lawrence Robert Dicksee - Accounting - 1897 - 99 pages
...contact of the circles. Q. 9.—Prove that the angle between a tangent to a circle and a chord through the point of contact is equal to the angle in the alternate segment. Show how to cut off from a given circle a segment to contain an angle equal to a given angle. Q. 10.—Prove...
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Key to Milne's Plane and Solid Geometry

William James Milne - Geometry - 1899 - 313 pages
...of Z ABC, and, Ex. 198, ZD is sup. of Z ABC; hence, § 54, Z ABE = Z D. Ex. 202. The angle between a tangent to a circle and a chord drawn from the point of contact is half the angle at the center subtended by that chord. Data : The circle whose center is O ; AB tangent...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 396 pages
...QED 232. Cor. A right angle is measured by one half a semicircum. ference. Ex. 202. The angle between a tangent to a circle and a chord drawn from the point of contact is half the angle at the center subtended by that chord. Ex. 203. A line which is tangent to the inner...
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