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Given: parllelogram ABCD circumscribe a circle
To prove: we know that pain syndrome from the extent part are equal in length.
AP=AS-------1
BP=BQ-------2
CR=CQ-------3
DR=DS-------4
Adding 1,2,3 and 4
AP+BP+CR+DR=AS+BQ+CQ+DS
AB+CD=AD+BC-------5
ABCD is a parllelogram
AB=CD
----------6
AD=BC
From 3 and 6 we get
AB+AB=AD+AD
2AB=2AD
AB=AD
If adjacent sides of parllelogram are equal then it becomes rhombus.
Hence ABCD is a Rhombus.
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