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350:{\displaystyle {\begin{array}{cl}\implies &\angle PG_{2}T=\angle PTG_{1}\\\implies &\triangle PTG_{2}\sim \triangle PG_{1}T\\\implies &{\frac {|PT|}{|PG_{2}|}}={\frac {|PG_{1}|}{|PT|}}\\\implies &|PT|^{2}=|PG_{1}|\cdot |PG_{2}|\end{array}}}
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The tangent-secant theorem can be proven using similar triangles (see graphic).
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Geometry theorem relating line segments created by a secant and tangent line
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526:{\displaystyle |PT|^{2}=|PG_{1}|\cdot |PG_{2}|}
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1248:The Quadrature of the Parabola
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1378:Doctrine of proportionality
606:, pp. 415-417 (German)
596:Schülerduden - Mathematik I
540:intersecting chords theorem
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1207:On the Sphere and Cylinder
1160:On the Sizes and Distances
368:describes the relation of
1909:Ancient Greece portal
1898:
1713:Philosophy of mathematics
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1628:Ptolemy's table of chords
683:Ancient Greek mathematics
380:line with the associated
36:alternate segment theorem
1580:Aristarchus's inequality
1153:On Conoids and Spheroids
626:Power of a Point Theorem
1688:Ancient Greek astronomy
1501:Inscribed angle theorem
1491:Greek geometric algebra
1146:Measurement of a Circle
579:Revolutions in Geometry
1942:Theorems about circles
1922:Mathematics portal
1708:Non-Euclidean geometry
1663:Mouseion of Alexandria
1536:Tangent-secant theorem
1486:Geometric mean theorem
1471:Exterior angle theorem
1466:Angle bisector theorem
1170:On Sizes and Distances
618:Tangent Secant Theorem
548:power of point theorem
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366:tangent-secant theorem
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18:Secant-tangent theorem
1610:Pappus's area theorem
1546:Theorem of the gnomon
1423:Quadratrix of Hippias
1346:Circles of Apollonius
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1373:Diophantine equation
1363:Circumscribed circle
1180:On the Moving Sphere
629:auf cut-the-knot.org
577:Michael L. O'Leary:
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1912: •
1718:Neusis construction
1638:Spiral of Theodorus
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435:intersect at point
34:Beginning with the
1605:Menelaus's theorem
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1351:Apollonian circles
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635:Weisstein, Eric W.
563:. Springer, 2012,
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362:Euclidean geometry
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1282:Doubling the cube
1255:The Sand Reckoner
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1368:Commensurability
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1277:Angle trisection
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375:
372:created by a
371:
370:line segments
367:
363:
333:
329:
325:
317:
307:
303:
299:
291:
286:
276:
273:
246:
243:
226:
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194:
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146:
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127:
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92:
88:
84:
81:
75:
72:
67:
63:
59:
37:
32:
19:
1913:
1900:
1742:Thomas Heath
1733:
1616:
1600:Law of sines
1456:
1388:Golden ratio
1253:
1246:
1237:
1231:(Theodosius)
1227:
1219:
1212:
1205:
1198:
1189:
1179:
1173:(Hipparchus)
1169:
1159:
1151:
1144:
1135:
1125:
1117:
1112:(Apollonius)
1108:
1100:
1088:
1063:Zeno of Elea
823:Eratosthenes
813:Dionysodorus
641:
625:
617:
595:
578:
560:
537:
534:
441:
412:
403:
396:
390:
365:
359:
1809:mathematics
1617:Arithmetica
1214:Ostomachion
1183:(Autolycus)
1102:Arithmetica
878:Hippocrates
808:Dinostratus
793:Dicaearchus
723:Aristarchus
1861:Babylonian
1761:arithmetic
1727:History of
1556:Apollonius
1241:(Menelaus)
1200:On Spirals
1119:Catoptrics
1058:Xenocrates
1053:Thymaridas
1038:Theodosius
1023:Theaetetus
1003:Simplicius
993:Pythagoras
978:Posidonius
963:Philonides
923:Nicomachus
918:Metrodorus
908:Menaechmus
863:Hipparchus
853:Heliodorus
803:Diophantus
788:Democritus
768:Chrysippus
738:Archimedes
733:Apollonius
703:Anaxagoras
695:(timeline)
554:References
1322:Inscribed
1082:Treatises
1073:Zenodorus
1033:Theodorus
1008:Sosigenes
953:Philolaus
938:Oenopides
933:Nicoteles
928:Nicomedes
888:Hypsicles
783:Ctesibius
773:Cleomedes
758:Callippus
743:Autolycus
728:Aristotle
708:Anthemius
643:MathWorld
538:Like the
498:⋅
318:⋅
263:⟹
155:⟹
131:△
128:∼
109:△
103:⟹
79:∠
57:∠
51:⟹
1936:Category
1886:Japanese
1871:Egyptian
1814:timeline
1802:timeline
1790:timeline
1785:geometry
1778:timeline
1773:calculus
1766:timeline
1754:timeline
1457:Elements
1303:Concepts
1265:Problems
1238:Spherics
1228:Spherics
1193:(Euclid)
1139:(Euclid)
1136:Elements
1129:(Euclid)
1090:Almagest
998:Serenus
973:Porphyry
913:Menelaus
868:Hippasus
843:Eutocius
818:Domninus
713:Archytas
542:and the
391:Elements
1866:Chinese
1821:numbers
1749:algebra
1677:Related
1651:Centers
1447:Results
1317:Central
988:Ptolemy
983:Proclus
948:Perseus
903:Marinus
883:Hypatia
873:Hippias
848:Geminus
838:Eudoxus
828:Eudemus
798:Diocles
638:"Chord"
573:175-176
378:tangent
1881:Indian
1658:Cyrene
1190:Optics
1109:Conics
1028:Theano
1018:Thales
1013:Sporus
958:Philon
943:Pappus
833:Euclid
763:Carpus
753:Bryson
602:
589:, p.
585:
571:, pp.
567:
386:Euclid
382:circle
376:and a
374:secant
364:, the
1876:Incan
1797:logic
1573:Other
1341:Chord
1334:Axiom
1312:Angle
968:Plato
858:Heron
778:Conon
1838:list
1126:Data
898:Leon
748:Bion
600:ISBN
583:ISBN
565:ISBN
431:and
410:and
1740:by
1454:In
591:161
394:.
388:'s
360:In
38:,
1938::
640:.
550:.
675:e
668:t
661:v
646:.
520:|
514:2
510:G
506:P
502:|
494:|
488:1
484:G
480:P
476:|
472:=
467:2
462:|
457:T
454:P
450:|
437:P
433:t
429:g
425:T
421:t
416:2
413:G
407:1
404:G
399:g
340:|
334:2
330:G
326:P
322:|
314:|
308:1
304:G
300:P
296:|
292:=
287:2
282:|
277:T
274:P
270:|
251:|
247:T
244:P
240:|
233:|
227:1
223:G
219:P
215:|
208:=
201:|
195:2
191:G
187:P
183:|
176:|
172:T
169:P
165:|
147:T
142:1
138:G
134:P
123:2
119:G
115:T
112:P
93:1
89:G
85:T
82:P
76:=
73:T
68:2
64:G
60:P
20:)
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