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" 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. "
Elements of Geometry and Trigonometry - Page 64
by Adrien Marie Legendre - 1837 - 359 pages
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...angle GAD. The tanand the line AC bisects the PROBLEM XV. To inscribe a circle in a given triangle. B Let ABC be the given triangle. Bisect the angles A...B, by the lines AO and BO, meeting in the point O (Prob. V.) ; from the point 0 D, A F let fall the perpendiculars 0Z', OE, OF, on the sides of the triangle...
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874 - 424 pages
...will be on the circumference. PRORLEM 12. To inscribe a given regtdar polygon in a circle. PRORLEM 13. To inscribe a circle in a given triangle. Let ABC be the given triangle. n Draw the bisectrices AD and BE of the angles A and B [II. Prob. 5] ; from the intersection 0, draw...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874 - 234 pages
...therefore the angle T is cqu.il to the an^le A. (I. 23, eor.6.) QEF . PROP. IV.— PROBLEM. (Euc. IV. 4.) 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 straight lines BO and CO...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 378 pages
...MLN= L EDF. Thus a A , equiangular to A DEF, is described about the . QEF PROPOSITION IV. PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given A . It is required to inscribe a in the A ABC. Bisect L a ABC, ACB by the st. lines BO, CO, meeting...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...for the circumference, whose centre is D, intersects the given circumference in two points. PROBI.EM 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 any two angles B and C by the lines BD, CD, meeting...
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...circumference. Problem, To circumscribe a circle about a given triangle. C BOOK H.] THE CIRCLE. XXXIII. Problem. To inscribe a circle in a given triangle. Let ABC be the given triangle. SOLUTION. Bisect any two angles, A and B, by lines meeting in D. From D draw DE, DF, and DG per- c...
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An elementary treatise on geometrical drawing

John Henry Robson - 1880 - 114 pages
...divided into 2*, 2 J , a 4 , or generally 2" equal parts, it may be done by successive bisection. 10. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles at B and C. Let these bisectors intersect in O. Draw OD perpendicular to BC. With center O and radius...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...equiangular to the triangle DEF, and it is described about the circle ABC. QEF PROPOSITION 4. 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, ACB, by the straight...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - Euclid's Elements - 1881 - 236 pages
...proposition in this way will form a nseful exercise to the student. PROP. IV. PROBLEM. To intcribe a circle in a given triangle, Let ABC be the given triangle. It is required to inscribe a circle in it Bisect the angles ABC and BCA by the straight lines BD and...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...any point without a given circle, two equal tangents to the circle can be drawn. PROBLEM XVII. 235. To inscribe a circle in a given triangle. Let ABC be the given A. Bisect the Z. ABC and CAB. The bisectors meet in some point, as 0. From 0 draw OF, OD, and OE,...
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