| 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 - 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... | |
| 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... | |
| 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
...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 - 1022 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
...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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