Knowledge

Tangential triangle

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A right triangle has no tangential triangle, because the tangent lines to its circumcircle at its acute vertices are parallel and thus cannot form the sides of a triangle.
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of the reference triangle. That is, the lines connecting the vertices of the tangential triangle and the corresponding vertices of the reference triangle are
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of the tangential triangle coincides with the circumcircle of the reference triangle.
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The tangent lines containing the sides of the tangential triangle are called the
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Triangle formed by tangents to a given triangle's circumcircle at its vertices
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of the reference triangle. Any two of these are concurrent with the third
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Smith, Geoff, and Leversha, Gerry, "Euler and triangle geometry",
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of the tangential triangle is on the reference triangle's
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A reference triangle and its tangential triangle are in
225:, and the circumcircle of the tangential triangle are 379: 362: 217:The reference triangle's circumcircle, its 369: 355: 134:) is the triangle whose sides are on the 311:, Dover Publications, 2007 (orig. 1929). 285:, Dover Publications, 2007 (orig. 1952). 18: 191:, and the axis of perspectivity is the 169:(whose vertices are at the feet of the 380: 301: 321: 277: 275: 273: 271: 269: 165:of the tangential triangle and the 13: 14: 404: 288: 266: 325: 388:Objects defined for a triangle 235:The reference triangle is the 1: 259: 341:. You can help Knowledge by 239:of the tangential triangle. 173:of the reference triangle). 142:at the reference triangle's 138:to the reference triangle's 7: 309:Advanced Euclidean Geometry 298:91, November 2007, 436–452. 242: 214:of the reference triangle. 176:The tangential triangle is 10: 409: 320: 281:Altshiller-Court, Nathan. 393:Elementary geometry stubs 94:homothetic transformation 27: Reference triangle 249:Tangential quadrilateral 337:-related article is a 115: 51: Orthic triangle 39: Circumcircle of 22: 296:Mathematical Gazette 163:center of similitude 335:elementary geometry 307:Johnson, Roger A., 124:tangential triangle 72:Tangential triangle 254:Tangential polygon 116: 92: Axes of the 350: 349: 237:Gergonne triangle 219:nine-point circle 203:of the triangle. 400: 371: 364: 357: 329: 322: 312: 305: 299: 292: 286: 283:College Geometry 279: 113: 109: 102: 91: 86: 79: 69: 64: 57: 50: 45: 38: 33: 26: 408: 407: 403: 402: 401: 399: 398: 397: 378: 377: 376: 375: 318: 316: 315: 306: 302: 293: 289: 280: 267: 262: 245: 201:symmedian point 182:orthic triangle 167:orthic triangle 126:of a reference 114: 111: 104: 97: 89: 87: 81: 74: 67: 65: 59: 52: 48: 46: 40: 36: 34: 28: 24: 17: 12: 11: 5: 406: 396: 395: 390: 374: 373: 366: 359: 351: 348: 347: 330: 314: 313: 300: 287: 264: 263: 261: 258: 257: 256: 251: 244: 241: 132:right triangle 130:(other than a 110:, centered at 88: 66: 47: 35: 23: 15: 9: 6: 4: 3: 2: 405: 394: 391: 389: 386: 385: 383: 372: 367: 365: 360: 358: 353: 352: 346: 344: 340: 336: 331: 328: 324: 323: 319: 310: 304: 297: 291: 284: 278: 276: 274: 272: 270: 265: 255: 252: 250: 247: 246: 240: 238: 233: 230: 228: 224: 220: 215: 213: 209: 204: 202: 198: 194: 190: 185: 183: 179: 174: 172: 168: 164: 160: 156: 151: 149: 145: 141: 137: 136:tangent lines 133: 129: 125: 121: 108: 101: 95: 85: 78: 73: 63: 56: 44: 32: 21: 343:expanding it 332: 317: 308: 303: 295: 290: 282: 234: 231: 223:polar circle 216: 208:exsymmedians 205: 193:Lemoine axis 186: 175: 161:, as is the 155:circumcenter 152: 140:circumcircle 123: 117: 106: 99: 83: 76: 71: 61: 54: 42: 30: 189:perspective 146:. Thus the 382:Categories 260:References 197:concurrent 178:homothetic 159:Euler line 212:symmedian 171:altitudes 243:See also 148:incircle 144:vertices 128:triangle 120:geometry 96:between 180:to the 227:coaxal 221:, its 122:, the 90:  70:  68:  49:  37:  25:  333:This 339:stub 153:The 103:and 118:In 107:DEF 100:GHI 84:ABC 80:of 77:DEF 62:ABC 58:of 55:GHI 43:ABC 31:ABC 384:: 268:^ 229:. 184:. 370:e 363:t 356:v 345:. 112:K 105:△ 98:△ 82:△ 75:△ 60:△ 53:△ 41:△ 29:△

Index


homothetic transformation
geometry
triangle
right triangle
tangent lines
circumcircle
vertices
incircle
circumcenter
Euler line
center of similitude
orthic triangle
altitudes
homothetic
orthic triangle
perspective
Lemoine axis
concurrent
symmedian point
exsymmedians
symmedian
nine-point circle
polar circle
coaxal
Gergonne triangle
Tangential quadrilateral
Tangential polygon

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