| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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);... | |
| 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... | |
| 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... | |
| 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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