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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. "
Elements of Geometry: With, Practical Applications - Page 147
by George Roberts Perkins - 1850 - 320 pages
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1892 - 468 pages
...(being inscribed in a semicircle). .-. EM is tangent to the circle at M. 239 PROPOSITION XXXVII. PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle. To inscribe a circle in the A ABC. H Construction. Bisect AA and C. 275 From E, the intersection...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...radius is the sum of the radii of the given circles. •••.. JK PROPOSITION XXXII.—PROBLEM. 80. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect any two of its angles, as B and C. by straight lines meeting in O. From the point O let fall perpendiculars...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 390 pages
...For since, by construction, AB = CD and AD = BC, ABCD is a parallelogram. ( 108.) PROPOSITION- XL. PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle. J To inscribe a circle in ABC. Draw AD and BE bisecting the angles A and B, respectively ( 207);...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...construction, AB = CD and AD = BC, ABCD is a parallelogram. ( 108.) PROPOSITION XL. PROBLEM. 221. To inscribe a circle in a given triangle. ,,< ' Let ABC be the given triangle. To inscribe a circle in ABC. Draw AD and BE bisecting the angles A and B~, respectively ( 207) ;...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...required. EXERCISES. I. Construct a square upon a given straight line. PROPOSITION XXIV. PROBLEM. 193. To inscribe a circle in a given triangle. Let ABC be the given triangle. To inscribe a circle in ABC. It is known (from 96) that the point in which the bisectors of the angles...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 278 pages
...centre of a given circle or of a given arc. BOOK II. PLANE GEOMETRY. PRO POSITION XXXVI. PROBI.KM. 315. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the AA and C. 304 From E, the intersection of the bisectors, draw EH to the side A C. 300 From...
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Mathematics, mechanics, heat

American School (Chicago, Ill.) - Engineering - 1903
...through any three given points ; or a circle circumscribed about a given triangle. PROBLEM XIII. 13. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect any two of its angles. With the point D, where the two bisecting lines meet, as a centre, with a radius...
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Elementary Geometry: Plane

James McMahon - Geometry, Plane - 1903 - 380 pages
...[Use the method and proof of 20.] INSCRIPTION AND CIRCUMSCRIPTION Inscribed circle. 101. PROBLEM 8. To inscribe a circle in a given triangle. Let ABC be the triangle in which it is required to inscribe a circle. Bisect any two of the internal angles, say B...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...called the circum-centre of the triangle. BOOK II. PLANE GEOMETRY. PROPOSITION XXXVI. PROBLEM. 315. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the AA and C. 304 From E, the intersection of the bisectors, draw EH J- to the side AC. 300 From...
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A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908
...point of intersection being the centre of the circle circumscribed about the triangle. PROBLEM 26. To inscribe a circle in a given triangle. Let ABC be the triangle, in which a circle is to be inscribed. Construction. Bisect the I.'ABC, ACB by the st. lines...
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