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Prove that any four vertices of a regula...

Prove that any four vertices of a regular pentagon are concyclic.

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Given: a regular pentagon ABCDE.
To prove: Any four vertices of the pentagon ABCDE are concyclic.
Construcation: Join BD and CE.
Proof : In `DeltaBCD` and `DeltaECD`, we have
`BC=ED` (sides of a regular pentagon)
`angleC=angleD` (angles of regular pentagon)
`CD=CD` (common sides)
`DeltaBCDcongDeltaCDE` (by SAS criterion of congruence)
`thereforeangle1- angle2`
But they are subtended by CD on the same of it.
`therefore` Points B,C,D,E are concyclic.
Similarly, it can be proved that any other four vertices of the pentagon ABCDE are concyclic.
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