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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 ... - Page 311
by Charles Hutton - 1831
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - Euclid's Elements - 1789 - 298 pages
...three equal parts, by any known method, which is purely geometrical. PROP. _J PROP. XXIV. THEOREM. The angle formed by a tangent to a circle and a chord drawn from the point of contacTr, is equal to the angle in the alterr nate fegment. Let EC be a tangent to the circle AFDE,...
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

John Bonnycastle - Euclid's Elements - 1803 - 470 pages
...divided into three equal parts, by any known method, which is purely geometrical. PROP. XXIV. THEOREM. The angle formed by a tangent to a circle and a chord...of contact, is equal to the angle in the alternate fegment. Let BC be a tangent to the circle AFDE, and AB a chord drawn from the point of contaft ; then...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811
...(corol. 4, th. 6 ; or corol. 2, th. 48). Therefore the angle D is a right angle. THEOREM THEOREM LIII. The Angle formed by a Tangent to a Circle, and a Chord drawn from the Point of Contact, ia Equal to the Angle . in the Alternate Segment. IF AB be a tangent, and AC a chord, and D any angle...
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Encyclopaedia Perthensis; or, Universal dictionary of Knowledge ..., Volume 10

Encyclopaedia Perthensis - 1816 - 764 pages
...tothe three anpk-s BDC, DBC and DCB, that is to two *-ipht angles. (Th-. ta ) THEOR. XXIV. fa. 50. The angle formed by a tangent to a circle, and a chord drawn to the point of contatt, is equal to the angle in the alternate fegment of the circle Let AB be a tangent,...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 pages
...th. 6 ; or eorol. 2, th. 48), ;iogle ii it a right angle. B Therefore the THEOREM 312 THEOREM Lin. THE Angle formed by a Tangent to a Circle, and a Chord...ADC ; then will the angle D be equal to the angle BAG made by the tangent and chord, of the arc AEC. For the angle D, at the circumference, is measured...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 272 pages
...therefore, AD touches the circlee : and because the angle which the chord makes with the tangent at the point of contact, is equal to the angle in the alternate segment of the circlef ; therefore, the angle BAD is equal to the angle in the alternate segment AHB ; but...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...include the same portion of the circumference. PROPOSITION XV. THEOREM. a The angle formed by a tangent, and a chord drawn from the point of contact, is equal to an angle in the alternate segment of the circle ; that is, to an inscribed angle subtended by the arc...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...adjacent angles are equal, they are right angles. PROPOSITION XXXII. THKOREM. The angles contained by a tangent to a circle, and a chord drawn from the point of contact, are equal to the angles in the alternate segments of the circleLet EF be a tangent to the circle ABCD,...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 434 pages
...contact. PLANE GEOMETRY. PROPOSITION LV — THEOREM. The angle ABD, formed by a tangent AB, and a chord DB drawn from the point of contact, is equal to the angle in the alternate segment BED, and is measured by half the intercepted arc BD. For (figure last Prop.), let DE be || to AB, then...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...by half the entire circumference, which is the measure of two right angles. PROPOSITION IX. THEOEEM. The angle formed by a tangent to a circle, and a chord...angle in the alternate segment. If AB be a tangent, AC a chord, and D any angle in the alternate segment ADC ; then will the angle D be equal to the angle...
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