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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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Mensuration, Mechanical Powers and Machinery: The Principles of Mensuration ...

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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Elementary Geometry: With Applications in Mensuration

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...the angles A and B by the lines AO and BO, meeting at the point 0. From O, let fall the perpendiculars OD, OE, OF, on the three sides of the triangle...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 236 pages
...tangent to the circle (Bk. II. Th. v). PROBLEM XIX. To inscribe a circle in a given triangle. Let AB C be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point O. Prom O, let fall the perpendiculars OD, F OE, OF, on the three sides of the triangle...
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Elements of Geometry: With, Practical Applications

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 from...
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Mensuration, Mechanical Powers, and Machinery: The Principles of Mensuration ...

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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...there 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...and B, by the lines AO and BO, meeting in the point 0 (PROB. 5); from the point 0, let fall " the perpendiculars OD, OE, OF (PROB. 3), on the three sides...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 334 pages
...will be tangent to the circle (Bk- 11- Th- v)PROBLEM XIX To Inscribe a c1rcle in a gIven triangleLet ABC be the given triangle Bisect the angles A and B by the lines AO and BO, meeting at the point O- From O, let fall the perpendiculars OD, OE, OF, on the three sides of the triangle...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

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...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...bisects the 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....B, by the lines AO and BO, meeting in the point O (PROB. 5); from the point O, let fall the perpendiculars O1), OE, OF (PKOB. 3), on the three sides...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 252 pages
...be drawn; 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...
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