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109:{\displaystyle {\overline {BM}}\perp {\overline {AC}},{\overline {EF}}\perp {\overline {BC}}}
214:), then the perpendicular to a side from the point of intersection of the diagonals always
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374:(i.e., they add up to 90°), and are therefore equal. Finally, the angles
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that intercept the same arc of the circle (CD). Furthermore, the angles
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181:{\displaystyle \Rightarrow |{\overline {AF}}|=|{\overline {FD}}|}
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502:. Washington, DC: Math. Assoc. Amer., p. 59, 1967
476:The Birth of Mathematics: Ancient Times to 1300
244:be four points on a circle such that the lines
252:are perpendicular. Denote the intersection of
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565:Theorems about quadrilaterals and circles
218:the opposite side. It is named after the
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478:. Publisher Infobase Publishing.
288:. Then, the theorem states that
280:be the intersection of the line
264:. Drop the perpendicular from
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474:Michael John Bradley (2006).
429:is an isosceles triangle, so
346:, first note that the angles
354:are equal, because they are
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409:goes similarly: the angles
272:, calling the intersection
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323:. We will prove that both
18:Brahmagupta's theorem
445:, as the theorem claims.
536:"Brahmagupta's theorem"
228:More specifically, let
315:We need to prove that
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188:
182:
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522:Brahmagupta's Theorem
455:Brahmagupta's formula
390:, and thus the sides
382:are the same. Hence,
331:are in fact equal to
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197:Brahmagupta's theorem
183:
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311:Proof of the theorem
220:Indian mathematician
201:cyclic quadrilateral
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516:Brahmagupta theorem
498:; Greitzer, S. L.:
533:Weisstein, Eric W.
500:Geometry Revisited
437:. It follows that
425:are all equal, so
388:isosceles triangle
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496:Coxeter, H. S. M.
199:states that if a
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560:Brahmagupta
398:are equal.
225:(598-668).
223:Brahmagupta
554:Categories
484:0816054231
462:References
541:MathWorld
370:to angle
366:are both
212:diagonals
169:¯
141:¯
123:⇒
102:¯
89:⊥
84:¯
66:¯
53:⊥
48:¯
449:See also
294:midpoint
193:geometry
292:is the
216:bisects
482:
386:is an
276:. Let
303:Proof
480:ISBN
421:and
394:and
378:and
362:and
350:and
327:and
256:and
248:and
240:and
524:at
427:DFM
423:DMF
419:BME
415:BCM
411:FDM
384:AFM
380:FMA
376:CME
372:BCM
364:CME
360:CBM
352:CBM
348:FAM
260:by
203:is
191:In
556::
538:.
443:FD
441:=
439:AF
435:FM
433:=
431:FD
417:,
413:,
407:FM
405:=
403:FD
396:FM
392:AF
344:FM
342:=
340:AF
335:.
333:FM
329:FD
325:AF
321:FD
319:=
317:AF
299:.
297:AD
286:AD
282:EM
270:BC
258:BD
254:AC
250:BD
246:AC
236:,
232:,
195:,
544:.
290:F
278:F
274:E
266:M
262:M
242:D
238:C
234:B
230:A
175:|
165:D
162:F
155:|
151:=
147:|
137:F
134:A
127:|
98:C
95:B
80:F
77:E
71:,
62:C
59:A
44:M
41:B
20:)
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