 | William Grier - Mechanical engineering - 1842 - 320 pages
...angle C. 50. If ABC or ADC be a semicircle, then any angle D in that semicircle, is a right angle. 51. If AB be a tangent, and AC a chord, and D any angle in the alternate segment ADC ; then will the angle D be equal to the angle BAC made by the tangent and chord of the arc AEC. 53.... | |
 | Scottish school-book assoc - 1845 - 444 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... | |
 | George Roberts Perkins - Geometry - 1847 - 326 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... | |
 | Anthony Nesbit - Measurement - 1859 - 494 pages
...circumference, if both stand on the same base. 11. Any angle in a semicircle is a right angle. 12. The angle formed by a tangent to a circle, and a chord...contact, is equal to the angle in the alternate segment. 13. The sum of any two opposite angles of a quadrangle, inscribed in a circle, is equal to two right... | |
 | Euclides - 1860 - 288 pages
...adjacent angles are equal, they are right angles. PROPOSITION XXXII. THEOREM. 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 circle. Given EF a tangent to the circle ABCD,... | |
 | Charles Hutton - Mathematics - 1860 - 1020 pages
...angle (cor. 4, th, 6; or cor. 2, th. 48). Therefore iliu angle 1) is a right angle. 384 THEOREM LUI. The angle formed by a tangent to a circle, and a chord drawn fftm the pat of contact, is equal to the angle in the alternate segment. If AB be a ¿angent, and AC... | |
 | William Grier - Mechanical engineering - 1861 - 316 pages
...angle C. 50. If ABC or ADC be a semicircle, then any angle D in that semicircle, is a right angle. 51. If AB be a tangent, and AC a chord, and D any angle in the alternate segment A.DC ; then will the angle D be equal to the angle BAG made by the tangent and chord of the arc AEG. 52.... | |
 | General Medical Council (Great Britain) - 1866 - 496 pages
...possess ? HIGHER MATHEMATICS. 1. Inscribe a circle in a given sector of a circle. 2. 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 circle. 3. To describe a square that shall... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...of a right angle (Cor. 4, th. 6 ; or Cor. 2, th. 8). Therefore the angle D is a right angle. THEOREM The angle formed by a tangent to a circle, and a chord...chord, and D any angle in the alternate segment ADC, then will the angle D be equal to the angle BAC made by the tangent and chord of the arc AEC. For the... | |
 | Manchester univ - 1872 - 380 pages
...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 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. 
