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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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Elements of Geometry and Trigonometry Translated from the French of A.M ...

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...
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Elements of Geometry and Conic Sections

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...
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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 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...
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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
...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 fall...
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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
...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 fall...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...LMN is 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 Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...LMN is 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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