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" 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 Synopsis of Elementary Results in Pure and Applied Mathematics - Page xiv
by George Shoobridge Carr - 1880
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

John Bonnycastle - Euclid's Elements - 1803 - 470 pages
...purely geometrical. PROP. XXIV. THEOREM. 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 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: For the Use of Academies as Well as Private Tuition

Charles Hutton - Mathematics - 1812 - 620 pages
...B Therefore the THEOREM THEOREM LIII. 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. If AB be a tangent, and AC a chord, and D any angle in the alternate segment ADC ; A^ ~R then will...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 pages
...Therefore the THEOREM 312 THEOREM Lin. 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. If AB be a tangent, and AC a chord, and D any angle in the alternate segment ADC ; then will the angle...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 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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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...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 - 326 pages
...right angles. PROPOSITION IX. THEOEEM. 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. If AB be a tangent, AC a chord, and D any angle in the alternate segment ADC ; then will the angle...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...the angle D is a right angle. THEOREM 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. If AB be a tangent, and AC a chord, and D any angle in the alternate segment ADC, then will the angle...
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The Calendar of Owens college, Manchester

Manchester univ - 1872 - 380 pages
...segment of the outer circle. 8. Define a tangent. Show that the angle contained between a tangent and the chord from the point of contact is equal to the angle in the alternate segment of the circle. 9. Divide a given straight line into two parts, so that the squai'cs on the whole line...
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The elementary geometry of the right line and circle

William Alexander Willock - Circle - 1875 - 196 pages
...circle, and is tlte tangent, as stateil. 16. 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. Let AM be the tangent at A in the circle R, and AB the chord, making any angle, a, with AM, and also...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...the circumference. Therefore, С A is perpendicular to D A. THEOREM XXXVII. The angle contained by a tangent and a chord from the point of contact is equal to the angle in the opposite segment. Let AD be the tangent, and А С the chord ; let AB be the diameter through A, and...
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