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" 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. "
Mathematics, mechanics, heat - Page 70
by American School (Chicago, Ill.) - 1903
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...CAD. The tangents are therefore equal, and the line AC bisects the angle between them. 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 A 0 and BO, meeting in the p9int O (Prob. V.) ; from the point 0 let...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1873 - 292 pages
...circumscribed about a given triangle. PROBLEM XIII. 16 To inscr<be a circle in a given triangle. Let А B С be the given triangle. Bisect any two of its angles....of the sides, describe a circle, and it will be the circle required. Draw the perpendicular DE, DF, DG. The angles at A are equal by construction, and...
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874 - 428 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 Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 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 And Trigonometry

Charles Davies - 1874 - 464 pages
...CAD. The tangents are therefore equal, and the line AC bisects the angle between them. PROBLEM XV. To inscribe a circle in a given triangle. Let ABC be the g1ven triangle. Bisect the angles A and B, by the lines A 0 and BO, meeting in the point 0 (Prob. V.)...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin SMITH - 1876 - 382 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 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 - 118 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...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 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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