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opposing angles in a cyclic quadrilateral are supplementary
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(Theorem)
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Proof. Let  be a quadrilateral inscribed in a circle
Note that
 subtends arc  and
 subtends arc  . Now, since a circumferential angle is half the corresponding central angle, we see that
 is one half of the sum of the two angles  at  . But the sum of these two angles is
 , so that
Similarly, the sum of the other two opposing angles is also
 . 
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"opposing angles in a cyclic quadrilateral are supplementary" is owned by rm50.
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Cross-references: circumferential angle is half the corresponding central angle, arc, sum, angles, opposite, circle, inscribed, quadrilateral
There are 2 references to this entry.
This is version 5 of opposing angles in a cyclic quadrilateral are supplementary, born on 2007-06-07, modified 2007-07-27.
Object id is 9552, canonical name is OpposingAnglesInACyclicQuadrilateralAreSupplementary.
Accessed 1394 times total.
Classification:
| AMS MSC: | 51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries) |
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Pending Errata and Addenda
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