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217:
149:
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223:
The point of intersection of the diagonals is located towards the sides of the quadrilateral to proportional distances to the length of these sides.
142:
The point of intersection of the diagonals is located towards the sides of the quadrilateral to proportional distances to the length of these sides.
865:
251:
294:
269:
Gallatly, W. "The
Harmonic Quadrilateral." §124 in The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, pp. 90 and 92, 1913.
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39:) in which the products of the lengths of opposite sides are equal. It has several important properties.
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16:
Cyclic quadrilateral in which the products of opposite side lengths are equal
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either intersect at one point or are mutually parallel.
711:
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363:
315:
155:Tangents to the circumscribed circle at points
70:Tangents to the circumscribed circle at points
82:either intersect at one point or are mutually
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35:that can be inscribed in a circle (
14:
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192:
172:
148:
51:be a harmonic quadrilateral and
199:The bisectors of the angles at
100:The bisectors of the angles at
1:
838:. You can help Knowledge by
244:Advanced Euclidean Geometry
242:Johnson, Roger A. (2007) ,
906:
817:
207:intersect on the diagonal
119:of the quadrilateral is a
108:intersect on the diagonal
885:Types of quadrilaterals
246:, Dover, p. 100,
163:and the straight line
78:and the straight line
25:harmonic quadrilateral
528:Nonagon/Enneagon (9)
458:Tangential trapezoid
37:cyclic quadrilateral
640:Megagon (1,000,000)
408:Isosceles trapezoid
29:harmonic quadrangle
610:Icositetragon (24)
131:in the triangles ∆
21:Euclidean geometry
847:
846:
812:
811:
653:
652:
630:Myriagon (10,000)
615:Triacontagon (30)
579:Heptadecagon (17)
569:Pentadecagon (15)
564:Tetradecagon (14)
503:Quadrilateral (4)
373:Antiparallelogram
253:978-0-486-46237-0
123:of the angles at
897:
868:
861:
854:
832:geometry-related
826:
819:
625:Chiliagon (1000)
605:Icositrigon (23)
584:Octadecagon (18)
574:Hexadecagon (16)
478:
297:
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559:Tridecagon (13)
549:Hendecagon (11)
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438:Right trapezoid
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264:Further reading
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890:Geometry stubs
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764:Pseudotriangle
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554:Dodecagon (12)
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834:article is a
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804:Weakly simple
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744:Infinite skew
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659:Star polygons
656:
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645:Apeirogon (∞)
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589:Icosagon (20)
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423:Parallelogram
421:
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418:Orthodiagonal
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398:Ex-tangential
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33:quadrilateral
30:
26:
22:
840:expanding it
829:
814:
598:>20 sides
533:Decagon (10)
518:Heptagon (7)
508:Pentagon (5)
498:Triangle (3)
402:
393:Equidiagonal
243:
237:
46:
28:
24:
18:
794:Star-shaped
769:Rectilinear
739:Equilateral
734:Equiangular
698:Hendecagram
542:11–20 sides
523:Octagon (8)
513:Hexagon (6)
488:Monogon (1)
330:Equilateral
115:A diagonal
879:Categories
799:Tangential
703:Dodecagram
481:1–10 sides
472:By number
453:Tangential
433:Right kite
229:References
187:are equal.
97:are equal.
43:Properties
779:Reinhardt
688:Enneagram
678:Heptagram
668:Pentagram
635:65537-gon
493:Digon (2)
463:Trapezoid
428:Rectangle
378:Bicentric
340:Isosceles
317:Triangles
121:symmedian
754:Isotoxal
749:Isogonal
693:Decagram
683:Octagram
673:Hexagram
474:of sides
403:Harmonic
304:Polygons
84:parallel
66:. Then:
61:diagonal
57:midpoint
774:Regular
719:Concave
712:Classes
620:257-gon
443:Rhombus
383:Crossed
179:Angles
89:Angles
31:, is a
784:Simple
729:Cyclic
724:Convex
448:Square
388:Cyclic
350:Obtuse
345:Kepler
250:
830:This
759:Magic
355:Right
335:Ideal
325:Acute
135:and ∆
27:, or
836:stub
789:Skew
413:Kite
308:List
248:ISBN
203:and
185:∠DMC
183:and
181:∠BMC
159:and
127:and
104:and
95:∠DMC
93:and
91:∠BMC
74:and
55:the
49:ABCD
47:Let
23:, a
137:ADC
133:ABC
59:of
19:In
881::
209:AC
165:BD
117:BD
110:AC
80:BD
64:AC
867:e
860:t
853:v
842:.
310:)
306:(
296:e
289:t
282:v
211:.
205:D
201:B
161:C
157:A
139:.
129:D
125:B
112:.
106:D
102:B
86:.
76:C
72:A
53:M
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