Since ABCD is a parallelogram circumscribed in a circle
AB=CD........(1)
BC=AD........(2)
DR=DS (Tangents on the circle from same point D)
CR=CQ(Tangent on the circle from same point C)
BP=BQ (Tangent on the circle from same point B )
AP=AS (Tangents on the circle from same point A)
Adding all these equations we get
DR+CR+BP+AP=DS+CQ+BQ+AS
(DR+CR)+(BP+AP)=(CQ+BQ)+(DS+AS)
CD+AB=AD+BC
Putting the value of equation 1 and 2 in the above equation we get
2AB=2BC
AB=BC...........(3)
From equation (1), (2) and (3) we get
AB=BC=CD=DA
∴ABCD is a Rhombus
0 comments:
Post a Comment