| Matthew Iley - 1820 - 512 pages
...at right angles. Then join AB, BD, DC, and CA ; the figure ABCD is the square required. PROBLEM III. **To inscribe a circle in a given triangle. Let ABC be the** triangle in which ii is required to inscribe a circle. About the angular points B and C, with any convenient... | |
| Euclid - 1826 - 234 pages
...triangle equiangular to the triangle DEF. Therefore about a given circle, &c. QEF I PROPOSITION IV. **PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle;** it is required to inscribe a circle in the triangle ABC. Bisect the angles ABC, AC в, by the right... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...CB=CD ; hence they are equal ; hence AD is equal to AB, and also the angle CAD to CAB. PROBLEM. 1 53. **To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the** angles A and B, by the lines AO and BO, meeting in the point O ; from the point O, let fall the perpendiculars... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...bisects the angle formed by two tangents, must pass through the centre .of the circle. PROBLEM XV. **To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the** angles A and B, by the lines AO and BO, meeting in the point O ; from the point O, let fall the perpendiculars... | |
| Nathan Scholfield - 1845 - 894 pages
...segment would be a semicircle; and consequently the centre would be the middle of AB. PROBLEM XVIII. **To inscribe a circle in a given triangle. • Let ABC be the given triangle. Bisect the** angles A and B, by the lines AO and BO, meeting in the point O ; from the point O, let fall the perpendiculars... | |
| Charles Davies - Geometrical drawing - 1846 - 254 pages
...point of intersection, draw the lines AD and CD, and ABCD will be the required rhombus. 42. How do you **inscribe a circle in a given triangle? Let ABC be the given triangle. Bisect** either two of the angles, as A and C, by the lines AO and CO, and the point of intersection O will... | |
| Euclides - 1846 - 292 pages
...equiangular to the given triangle DEF, and it is described about the given circle ABC. QEF PROP. IV. PBOB. **To inscribe a circle in a given triangle. Let ABC be the given triangle** : it is required to inscribe a circle in the triangle ABC. Bisect the angles ABC, ACB by the straight... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...the two triangles AFG, AFH, we see that the angles AGF and AHF are equal, each being a right angle ; **also the angles FAG, FAH are equal, since AF bisects...and consequently be the inscribed circle required.** Cor. The three lines bisecting the three angles of a triangle meet at the same point, which point is... | |
| Thomas Tate (mathematical master.) - 1848 - 284 pages
...Cor. 3. Regular polygons are not only equilateral, but also equiangular ; thus, /ABC=Z.BCD — &c. 69. **PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle; bisect** A the angles BCA and CBA (Art. 21.) by the lines CD and BD meeting each other in the point D; from... | |
| Daniel Adams - Arithmetic - 1849 - 142 pages
...and the radius DE, describe a circle, and it will be inscribed in the given polygon. PROBLEM XXXIII. **To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect** any two angles, as A and B, and the point D, where the bisecting lines cross each other, will be the... | |
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