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Equidistant

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140: 32: 129: 296:(lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points. 232:
is equidistant from all four vertices, and it is equidistant from two opposite sides and also equidistant from the other two opposite sides. A point on the
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of a line segment. The point where the red line crosses the black line segment is equidistant from the two end points of the black line segment.
262:) and a fixed line (the directrix), where distance from the directrix is measured along a line perpendicular to the directrix. 347: 151:
by the circle C. The circumcentre O is equidistant to each point on the circle, and a fortiori to each vertex of the polygon.
96: 68: 178:. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in 372: 266: 115: 304: 75: 221:
of a triangle or other polygon is equidistant from the two vertices at the ends of that side. Every point on the
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is equidistant from the points of tangency of the polygon's sides with the circle. Every point on a
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the set of points that are equidistant from and on one side of a given line form a
259: 233: 19:"Equidistance" redirects here. For the principle in maritime boundary claims, see 316: 237: 293: 225:
of any polygon is equidistant from the two sides that emanate from that angle.
206: 144: 387: 209:: the circumcentre is equidistant from each of the vertices. Likewise, the 198: 274: 128: 247:
is equidistant from every point on the circle. Likewise the center of a
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is the set of points in a plane equidistant from a fixed point (the
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of points equidistant from two given (different) points is their
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Point that is at the same distance to every object in a given set
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is a thin version of that shape that is equidistant from its
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between that point and each object in the set are equal.
182:the locus of points equidistant from two points in 56:. Unsourced material may be challenged and removed. 385: 335: 336:Clapham, Christopher; Nicholson, James (2009). 251:is equidistant from every point on the sphere. 201:is a point equidistant from each of the three 342:. Oxford University Press. pp. 164–165. 339:The concise Oxford dictionary of mathematics 367:(5th ed.), Brooks/Cole, p. 392, 116:Learn how and when to remove this message 138: 127: 386: 362: 54:adding citations to reliable sources 25: 13: 240:is equidistant between two sides. 219:perpendicular bisector of the side 14: 405: 30: 307:(which is a curve not a line). 41:needs additional citations for 356: 329: 1: 322: 159:from a set of objects if the 7: 310: 213:of a triangle or any other 10: 410: 18: 363:Smart, James R. (1997), 176:perpendicular bisector 155:A point is said to be 152: 136: 133:Perpendicular bisector 21:Equidistance principle 142: 131: 271:topological skeleton 223:bisector of an angle 50:improve this article 394:Elementary geometry 301:hyperbolic geometry 180:n-dimensional space 166:In two-dimensional 290:Euclidean geometry 215:tangential polygon 168:Euclidean geometry 153: 137: 365:Modern Geometries 349:978-0-19-923594-0 190:−1)-space. 126: 125: 118: 100: 401: 378: 377: 360: 354: 353: 333: 243:The center of a 234:axis of symmetry 228:The center of a 121: 114: 110: 107: 101: 99: 58: 34: 26: 409: 408: 404: 403: 402: 400: 399: 398: 384: 383: 382: 381: 375: 361: 357: 350: 334: 330: 325: 317:Equidistant set 313: 207:cyclic polygons 122: 111: 105: 102: 59: 57: 47: 35: 24: 17: 12: 11: 5: 407: 397: 396: 380: 379: 373: 355: 348: 327: 326: 324: 321: 320: 319: 312: 309: 294:parallel lines 267:shape analysis 186:-space is an ( 145:cyclic polygon 124: 123: 38: 36: 29: 15: 9: 6: 4: 3: 2: 406: 395: 392: 391: 389: 376: 374:0-534-35188-3 370: 366: 359: 351: 345: 341: 340: 332: 328: 318: 315: 314: 308: 306: 302: 297: 295: 291: 286: 284: 280: 276: 272: 268: 263: 261: 257: 252: 250: 246: 241: 239: 235: 231: 226: 224: 220: 216: 212: 208: 204: 200: 196: 191: 189: 185: 181: 177: 173: 169: 164: 162: 158: 150: 149:circumscribed 146: 141: 134: 130: 120: 117: 109: 98: 95: 91: 88: 84: 81: 77: 74: 70: 67: –  66: 65:"Equidistant" 62: 61:Find sources: 55: 51: 45: 44: 39:This article 37: 33: 28: 27: 22: 364: 358: 338: 331: 298: 287: 264: 253: 242: 227: 199:circumcentre 192: 187: 183: 165: 156: 154: 112: 103: 93: 86: 79: 72: 60: 48:Please help 43:verification 40: 275:medial axis 157:equidistant 106:August 2012 323:References 305:hypercycle 283:boundaries 76:newspapers 230:rectangle 161:distances 388:Category 311:See also 256:parabola 211:incentre 203:vertices 195:triangle 90:scholar 371:  346:  269:, the 249:sphere 245:circle 193:For a 170:, the 92:  85:  78:  71:  63:  279:shape 277:of a 260:focus 236:of a 172:locus 147:P is 97:JSTOR 83:books 369:ISBN 344:ISBN 238:kite 197:the 143:The 69:news 299:In 288:In 273:or 265:In 52:by 390:: 292:, 285:. 254:A 352:. 188:n 184:n 119:) 113:( 108:) 104:( 94:· 87:· 80:· 73:· 46:. 23:.

Index

Equidistance principle

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"Equidistant"
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Perpendicular bisector

cyclic polygon
circumscribed
distances
Euclidean geometry
locus
perpendicular bisector
n-dimensional space
triangle
circumcentre
vertices
cyclic polygons
incentre
tangential polygon
perpendicular bisector of the side
bisector of an angle

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