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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, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 378 pages
...also / 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 - 114 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 O and...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 400 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 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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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...any point without a given circle, two equal tangents to the circle can be drawn. PROBLEM XVII. 235. To inscribe a circle in a given triangle. Let ABC be the given A. Bisect the Z. ABC and CAB. The bisectors meet in some point, as 0. From 0 draw OF, OD, and OE,...
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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
...LMN is 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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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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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
...About a 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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