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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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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...AD is tangent to circle C (Gh. IV, Th. XI) ; similarly, AE is a second tangent. QK f. PROBLEM XXIII. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect any two angles, as A and B (Prob. VI), producing their bisectors till they meet in O; fnom O to the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 pages
...equiangular to the triangle DEF, and it is described about thedrcle ABC. QEF, PEOPOSITION 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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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 346 pages
...will be tangent to the circle (Bk. II. Th. v). ( PROBLEM XIX To 1nscribe a c1rcle in a g1ven tmang1r.. Let 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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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 331 pages
...circle whose radius is the sum of the radii of the given circles. 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 (7, by straight lines meeting in 0. From the point 0 let fall perpendiculars...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...given circle describe a quadrilateral equiangular to a given quadrilateral. PROPOSITION 4. PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given A ; it is reqd. to inscribe a 0 in it. Bisect the LS ABC, BCA by the st. lines BO, CO. From O draw...
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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
...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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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 - 274 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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