| Charles Davies - Trigonometry - 1849 - 384 pages
...which 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.** linn, we have the angle DAO=OAF, the right angle ADO = AFO ; hence the third angle AOD is equal to... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...for the circumference whose center is D intersects the given circumference in two points. PROBLEM xv. **To inscribe a circle in a given triangle. Let ABC be the given triangle;** it is required to inscribe a circle in it. Bisect the angles B and C by the lines BD, CD, meeting each... | |
| Daniel Adams - Measurement - 1850 - 144 pages
...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 center... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...lines AB, AC, must be situated in the line AD, which bisects the angle BAC. PROPOSITION III. .PROBLEM. **To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect** the angle BAC by the line AD; also bisect the angle ABC by the line BD, (B. I, Prop, xi.) Then, if... | |
| Charles Davies - Geometry - 1850 - 218 pages
...perpendicular to a radius at its extremity, they will be tangent to the circle (Bk. II. Th. v). PROBLEM XIX. **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 at the point 0. From O, let fall the perpendiculars... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...will be two equal tangents, AB, AD. The angles CAD, CAB, are also equal (B. 1., p. 17). PEOBLEM 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 0 (PROB. 5); from the point 0, let... | |
| Euclides - Geometry - 1853 - 334 pages
...given circle ABC, since each of its sides touches the circle. Which was to be done. PEOP. IV. THEOE. **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 (i. 9) the angles ABC, A BCA by the... | |
| Charles Davies - Geometry - 1854 - 436 pages
...angle formed by two tangents, must pass through the centre of tho circle. 84 GEOMETRY. 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 (PROB. 5); from the point O, let... | |
| Charles William Hackley - Engineering - 1855 - 482 pages
...radius DC, I escribe the circle C ef, as required. 80. To form a rectangle of greatest surface, in a icn **triangle. Let ABC be the given triangle ; bisect any two of its** sides, as AB, BC, in e and d; draw the line ed ; also, at right angles with the line ed, draw the lines... | |
| Charles Haslett - Engineering - 1856 - 530 pages
...distance or radius DC, describe the circle C ef, as required. 30. To form a rectangle of greatest surface, **in a given triangle. Let ABC be the given triangle ; bisect any two of its** sides, as AB, BC, in e and d'f draw tlie line e d', also, at right angles with the line ed, draw the... | |
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